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", "Text"], Cell[CellGroupData[{ Cell["a={{1,3},{3,1}}", "Input", CellLabel->"In[21]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3"}, {"3", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ Cell["Here is a non homogeneous part. ", "Text"], Cell[CellGroupData[{ Cell["b={1,4}", "Input", CellLabel->"In[22]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[22]="] }, Open ]] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,-3}", "Input", CellLabel->"In[23]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[23]="] }, Open ]], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[24]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-1\), "1"}, {"1", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[24]="] }, Open ]], Cell[CellGroupData[{ Cell["evals=Eigenvalues[a]", "Input", CellLabel->"In[25]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`{\(-2\), 4}\)], "Output", CellLabel->"Out[25]="] }, Open ]], Cell["Here is the form of the answer.", "Text"], Cell[CellGroupData[{ Cell["\<\ ans=Sum[c[i] Exp[evals[[i]] t] evs[[i]],{i,1,Length[a]}] - \ Inverse[a].b\ \>", "Input", CellLabel->"In[26]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\[ExponentialE]\^\(\(-2\)\ t\)\)\ \(c(1)\) + \[ExponentialE]\^\(4\ t\)\ \(c(2)\) - 11\/8, \[ExponentialE]\^\(\(-2\)\ t\)\ \(c(1)\) + \[ExponentialE]\^\(4\ t\)\ \(c(2)\) + 1\/8}\)], "Output", CellLabel->"Out[26]="] }, Open ]], Cell["\<\ Now all that remains is to evaluate the constants using the initial \ conditions\ \>", "Text"], Cell[CellGroupData[{ Cell["ans2=(ans/.t->0)-x0", "Input", CellLabel->"In[27]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{\(-\(c(1)\)\) + c(2) - 19\/8, c(1) + c(2) + 25\/8}\)], "Output", CellLabel->"Out[27]="] }, Open ]], Cell["\<\ Now we form the inner product of the above expressions which are \ equations that individually equal 0. This first example does need the \ solution to the adjoint problem, but others will so lets pretend that we need \ the adjoint eigenvectors. \ \>", "Text"], Cell[CellGroupData[{ Cell["evsad=Eigenvectors[Transpose[a]]", "Input", CellLabel->"In[28]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-1\), "1"}, {"1", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[28]="] }, Open ]], Cell["Now form the inner product", "Text"], Cell[CellGroupData[{ Cell["ans3=evsad.ans2", "Input", CellLabel->"In[29]:="], Cell[BoxData[ \(TraditionalForm\`{2\ \(c(1)\) + 11\/2, 2\ \(c(2)\) + 3\/4}\)], "Output",\ CellLabel->"Out[29]="] }, Open ]], Cell["Now solve these", "Text"], Cell[CellGroupData[{ Cell["\<\ ansend=Solve[ans3==Table[0,{j,1,Length[a]}],Table[c[i],{i,1,Length[\ a]}]]\ \>", "Input", CellLabel->"In[30]:="], Cell[BoxData[ \(TraditionalForm \`{{c(1) \[Rule] \(-\(11\/4\)\), c(2) \[Rule] \(-\(3\/8\)\)}}\)], "Output",\ CellLabel->"Out[30]="] }, Open ]], Cell["Here is the answer", "Text"], Cell[CellGroupData[{ Cell["ansfinal=ans/.ansend[[1]]", "Input", CellLabel->"In[31]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\(11\/8\)\) + \(11\ \[ExponentialE]\^\(\(-2\)\ t\)\)\/4 - \(3\ \[ExponentialE]\^\(4\ t\)\)\/8, 1\/8 - \(11\ \[ExponentialE]\^\(\(-2\)\ t\)\)\/4 - \(3\ \[ExponentialE]\^\(4\ t\)\)\/8}\)], "Output", CellLabel->"Out[31]="] }, Open ]], Cell["Check this with the built-in function", "Text"], Cell[CellGroupData[{ Cell["Table[x[i][t],{i,1,Length[a]}]", "Input", CellLabel->"In[32]:="], Cell[BoxData[ \(TraditionalForm\`{\((x(1))\) (t), \((x(2))\) (t)}\)], "Output", CellLabel->"Out[32]="] }, Open ]], Cell[CellGroupData[{ Cell["x0", "Input", CellLabel->"In[33]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[33]="] }, Open ]], Cell[CellGroupData[{ Cell["b", "Input", CellLabel->"In[34]:="], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[34]="] }, Open ]], Cell[CellGroupData[{ Cell["a", "Input", CellLabel->"In[35]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3"}, {"3", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[35]="] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ansdsolve=DSolve[{ 1+ x1[t] + 3*x2[t] - x1'[t]==0, 4+ 3*x1[t] + x2[t] - x2'[t]==0, x1[0]==1,x2[0]==-3 }, {x1[t], x2[t]}, t]\ \>", "Input", CellLabel->"In[36]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] 1\/8\ \[ExponentialE]\^\(\(-2\)\ t\)\ \((22 - 11\ \[ExponentialE]\^\(2\ t\) - 3\ \[ExponentialE]\^\(6\ t\))\), x2(t) \[Rule] 1\/8\ \[ExponentialE]\^\(\(-2\)\ t\)\ \((\(-22\) + \[ExponentialE]\^\(2\ t\) - 3\ \[ExponentialE]\^\(6\ t\))\)}}\)], "Output", CellLabel->"Out[36]="] }, Open ]], Cell[CellGroupData[{ Cell["FullSimplify[ansdsolve]", "Input", CellLabel->"In[37]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] 1\/8\ \(( \(-11\) + 22\ \[ExponentialE]\^\(\(-2\)\ t\) - 3\ \[ExponentialE]\^\(4\ t\))\), x2(t) \[Rule] 1\/8\ \(( 1 - 22\ \[ExponentialE]\^\(\(-2\)\ t\) - 3\ \[ExponentialE]\^\(4\ t\))\)}}\)], "Output", CellLabel->"Out[37]="] }, Open ]], Cell["Which matches the answer obtained from the expansion. 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Editable->False], TraditionalForm]], "Output", CellLabel->"Out[39]="] }, Open ]], Cell[CellGroupData[{ Cell["ansfinal", "Input", CellLabel->"In[40]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\(11\/8\)\) + \(11\ \[ExponentialE]\^\(\(-2\)\ t\)\)\/4 - \(3\ \[ExponentialE]\^\(4\ t\)\)\/8, 1\/8 - \(11\ \[ExponentialE]\^\(\(-2\)\ t\)\)\/4 - \(3\ \[ExponentialE]\^\(4\ t\)\)\/8}\)], "Output", CellLabel->"Out[40]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["We try a harder one ", "Text"], Cell[CellGroupData[{ Cell["a={{1,3},{2,1}}", "Input", CellLabel->"In[38]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3"}, {"2", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[38]="] }, Open ]], Cell[CellGroupData[{ Cell["Here is a non homogeneous part. ", "Text"], Cell[CellGroupData[{ Cell["b={1,4}", "Input", CellLabel->"In[39]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[39]="] }, Open ]] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,-3}", "Input", CellLabel->"In[40]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[40]="] }, Open ]], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[41]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-\@\(3\/2\)\), "1"}, {\(\@\(3\/2\)\), "1"} }], ")"}], TraditionalForm]], "Output", CellLabel->"Out[41]="] }, Open ]], Cell[CellGroupData[{ Cell["evals=Eigenvalues[a]", "Input", CellLabel->"In[42]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`{1 - \@6, 1 + \@6}\)], "Output", CellLabel->"Out[42]="] }, Open ]], Cell["Here is the form of the answer.", "Text"], Cell[CellGroupData[{ Cell["\<\ ans=Sum[c[i] Exp[evals[[i]] t] evs[[i]],{i,1,Length[a]}] - \ Inverse[a].b\ \>", "Input", CellLabel->"In[43]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\@\(3\/2\)\)\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\)\ \(c(1)\) + \@\(3\/2\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)\ \(c(2)\) - 11\/5, \[ExponentialE]\^\(\((1 - \@6)\)\ t\)\ \(c(1)\) + \[ExponentialE]\^\(\((1 + \@6)\)\ t\)\ \(c(2)\) + 2\/5}\)], "Output", CellLabel->"Out[43]="] }, Open ]], Cell["\<\ Now all that remains is to evaluate the constants using the initial \ conditions\ \>", "Text"], Cell[CellGroupData[{ Cell["ans2=(ans/.t->0)-x0", "Input", CellLabel->"In[44]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{\(-\@\(3\/2\)\)\ \(c(1)\) + \@\(3\/2\)\ \(c(2)\) - 16\/5, c(1) + c(2) + 17\/5}\)], "Output", CellLabel->"Out[44]="] }, Open ]], Cell["\<\ Now we form the inner product of the above expressions which are \ equations that individually equal 0. This first example does need the \ solution to the adjoint problem, but others will so lets pretend that we need \ the adjoint eigenvectors. \ \>", "Text"], Cell[CellGroupData[{ Cell["evsad=Eigenvectors[Transpose[a]]", "Input", CellLabel->"In[45]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-\@\(2\/3\)\), "1"}, {\(\@\(2\/3\)\), "1"} }], ")"}], TraditionalForm]], "Output", CellLabel->"Out[45]="] }, Open ]], Cell["Now form the inner product", "Text"], Cell[CellGroupData[{ Cell["ans3=evsad.ans2", "Input", CellLabel->"In[46]:="], Cell[BoxData[ \(TraditionalForm \`{c(1) + c(2) - \@\(2\/3\)\ \((\(-\@\(3\/2\)\)\ \(c(1)\) + \@\(3\/2\)\ \(c(2)\) - 16\/5)\) + 17\/5, c(1) + c(2) + \@\(2\/3\)\ \((\(-\@\(3\/2\)\)\ \(c(1)\) + \@\(3\/2\)\ \(c(2)\) - 16\/5)\) + 17\/5}\)], "Output", CellLabel->"Out[46]="] }, Open ]], Cell["Now solve these", "Text"], Cell[CellGroupData[{ Cell["\<\ ansend=Solve[ans3==Table[0,{j,1,Length[a]}],Table[c[i],{i,1,Length[\ a]}]]\ \>", "Input", CellLabel->"In[47]:="], Cell[BoxData[ \(TraditionalForm \`{{c(1) \[Rule] 1\/30\ \((\(-51\) - 16\ \@6)\), c(2) \[Rule] 1\/30\ \((\(-51\) + 16\ \@6)\)}}\)], "Output", CellLabel->"Out[47]="] }, Open ]], Cell["Here is the answer", "Text"], Cell[CellGroupData[{ Cell["ansfinal=ans/.ansend[[1]]", "Input", CellLabel->"In[48]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\(11\/5\)\) - \(\((\(-51\) - 16\ \@6)\)\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\)\)\/\(10\ \@6\) + \(\((\(-51\) + 16\ \@6)\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)\)\/\(10\ \@6\), 2\/5 + 1\/30\ \((\(-51\) - 16\ \@6)\)\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\) + 1\/30\ \((\(-51\) + 16\ \@6)\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)} \)], "Output", CellLabel->"Out[48]="] }, Open ]], Cell["Check this with the built-in function", "Text"], Cell[CellGroupData[{ Cell["Table[x[i][t],{i,1,Length[a]}]", "Input", CellLabel->"In[49]:="], Cell[BoxData[ \(TraditionalForm\`{\((x(1))\) (t), \((x(2))\) (t)}\)], "Output", CellLabel->"Out[49]="] }, Open ]], Cell[CellGroupData[{ Cell["x0", "Input", CellLabel->"In[50]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[50]="] }, Open ]], Cell[CellGroupData[{ Cell["b", "Input", CellLabel->"In[51]:="], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[51]="] }, Open ]], Cell[CellGroupData[{ Cell["a", "Input", CellLabel->"In[52]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3"}, {"2", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[52]="] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ansdsolve=DSolve[{ 1+ x1[t] + 3*x2[t] - Derivative[1][x1][t]==0, 4+ 2*x1[t] + x2[t] - Derivative[1][x2][t]==0, x1[0]==1,x2[0]==-3 }, {x1[t], x2[t]}, t]\ \>", "Input", CellLabel->"In[53]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] \(-\(\(44 - 32\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\) - 17\ \@6\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\) - 32\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\) + 17\ \@6\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)\)\/\(4\ \((\(-1\) + \@6)\)\ \((1 + \@6)\)\)\)\), x2(t) \[Rule] \(-\(\(\(-12\) + 51\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\) + 16\ \@6\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\) + 51\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\) - 16\ \@6\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)\)\/\(6\ \((\(-1\) + \@6)\)\ \((1 + \@6)\)\)\)\)}}\)], "Output", CellLabel->"Out[53]="] }, Open ]], Cell[CellGroupData[{ Cell["FullSimplify[ansdsolve]", "Input", CellLabel->"In[54]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] 1\/20\ \(( \(-44\) + \((32 - 17\ \@6)\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\) + \((32 + 17\ \@6)\)\ \[ExponentialE]\^\(t - \@6\ t\))\), x2(t) \[Rule] 1\/30\ \(( 12 + \((\(-51\) + 16\ \@6)\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\) - \((51 + 16\ \@6)\)\ \[ExponentialE]\^\(t - \@6\ t\))\)}}\)], "Output", CellLabel->"Out[54]="] }, Open ]], Cell["Which matches the answer obtained from the expansion. ", "Text"], Cell[CellGroupData[{ Cell["ansfinal", "Input", CellLabel->"In[55]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\(11\/5\)\) - \(\((\(-51\) - 16\ \@6)\)\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\)\)\/\(10\ \@6\) + \(\((\(-51\) + 16\ \@6)\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)\)\/\(10\ \@6\), 2\/5 + 1\/30\ \((\(-51\) - 16\ \@6)\)\ \[ExponentialE]\^\(\((1 - \@6)\)\ t\) + 1\/30\ \((\(-51\) + 16\ \@6)\)\ \[ExponentialE]\^\(\((1 + \@6)\)\ t\)} \)], "Output", CellLabel->"Out[55]="] }, Open ]], Cell[CellGroupData[{ Cell["testplot=N[ExpandAll[ansdsolve]]", "Input", CellLabel->"In[62]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] \(-2.20000000000000017`\) + 3.68206628136570124`\ 2.71828182845904509`\^\(\(-1.44948974278317788`\)\ t\) - 0.482066281365701065`\ 2.71828182845904509`\^\(3.44948974278317788`\ t\), x2(t) \[Rule] \(0.4`\[InvisibleSpace]\) - 3.00639452948436192`\ 2.71828182845904509`\^\(\(-1.44948974278317788`\)\ t\) - 0.393605470515637989`\ 2.71828182845904509`\^\(3.44948974278317788`\ t\)}}\)], "Output",\ CellLabel->"Out[62]="] }, Open ]], Cell["\<\ We can plot the answers. 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", "Text"], Cell[CellGroupData[{ Cell["b={1,4}", "Input", CellLabel->"In[2]:="], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[2]="] }, Open ]] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,-3}", "Input", CellLabel->"In[3]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[3]="] }, Open ]], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[4]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-\[ImaginaryI]\), "1"}, {"\[ImaginaryI]", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[4]="] }, Open ]], Cell[CellGroupData[{ Cell["evals=Eigenvalues[a]", "Input", CellLabel->"In[5]:="], Cell[BoxData[ \(TraditionalForm\`{\(-\[ImaginaryI]\), \[ImaginaryI]}\)], "Output", CellLabel->"Out[5]="] }, Open ]], Cell["Here is the form of the answer.", "Text"], Cell[CellGroupData[{ Cell["\<\ ans=Sum[c[i] Exp[evals[[i]] t] evs[[i]],{i,1,Length[a]}] - \ Inverse[a].b\ \>", "Input", CellLabel->"In[6]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\[ImaginaryI]\)\ \[ExponentialE]\^\(\(-\[ImaginaryI]\)\ t\)\ \(c(1)\) + \[ImaginaryI]\ \[ExponentialE]\^\(\[ImaginaryI]\ t\)\ \(c(2)\) - 4, \[ExponentialE]\^\(\(-\[ImaginaryI]\)\ t\)\ \(c(1)\) + \[ExponentialE]\^\(\[ImaginaryI]\ t\)\ \(c(2)\) + 1}\)], "Output", CellLabel->"Out[6]="] }, Open ]], Cell["\<\ Now all that remains is to evaluate the constants using the initial \ conditions\ \>", "Text"], Cell[CellGroupData[{ Cell["ans2=(ans/.t->0)-x0", "Input", CellLabel->"In[7]:="], Cell[BoxData[ \(TraditionalForm \`{\(-\[ImaginaryI]\)\ \(c(1)\) + \[ImaginaryI]\ \(c(2)\) - 5, c(1) + c(2) + 4}\)], "Output", CellLabel->"Out[7]="] }, Open ]], Cell["\<\ Now we form the inner product of the above expressions which are \ equations that individually equal 0. This first example does need the \ solution to the adjoint problem, but others will so lets pretend that we need \ the adjoint eigenvectors. \ \>", "Text"], Cell[CellGroupData[{ Cell["evsad=Eigenvectors[Transpose[a]]", "Input", CellLabel->"In[8]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"\[ImaginaryI]", "1"}, {\(-\[ImaginaryI]\), "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[8]="] }, Open ]], Cell["Now form the inner product", "Text"], Cell[CellGroupData[{ Cell["ans3=evsad.ans2", "Input", CellLabel->"In[9]:="], Cell[BoxData[ \(TraditionalForm \`{c(1) + \[ImaginaryI]\ \((\(-\[ImaginaryI]\)\ \(c(1)\) + \[ImaginaryI]\ \(c(2)\) - 5)\) + c(2) + 4, c(1) - \[ImaginaryI]\ \((\(-\[ImaginaryI]\)\ \(c(1)\) + \[ImaginaryI]\ \(c(2)\) - 5)\) + c(2) + 4}\)], "Output", CellLabel->"Out[9]="] }, Open ]], Cell["Now solve these", "Text"], Cell[CellGroupData[{ Cell["\<\ ansend=Solve[ans3==Table[0,{j,1,Length[a]}],Table[c[i],{i,1,Length[\ a]}]]\ \>", "Input", CellLabel->"In[10]:="], Cell[BoxData[ \(TraditionalForm \`{{c(1) \[Rule] \(-2\) + \(5\ \[ImaginaryI]\)\/2, c(2) \[Rule] \(-2\) - \(5\ \[ImaginaryI]\)\/2}}\)], "Output", CellLabel->"Out[10]="] }, Open ]], Cell["Here is the answer", "Text"], Cell[CellGroupData[{ Cell["ansfinal=ans/.ansend[[1]]", "Input", CellLabel->"In[11]:="], Cell[BoxData[ \(TraditionalForm \`{\(-4\) + \((5\/2 + 2\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(-\[ImaginaryI]\)\ t\) + \((5\/2 - 2\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\[ImaginaryI]\ t\), 1 - \((2 - \(5\ \[ImaginaryI]\)\/2)\)\ \[ExponentialE]\^\(\(-\[ImaginaryI]\)\ t\) - \((2 + \(5\ \[ImaginaryI]\)\/2)\)\ \[ExponentialE]\^\(\[ImaginaryI]\ t\)}\)], "Output", CellLabel->"Out[11]="] }, Open ]], Cell["Check this with the built-in function", "Text"], Cell[CellGroupData[{ Cell["Table[x[i][t],{i,1,Length[a]}]", "Input", CellLabel->"In[12]:="], Cell[BoxData[ \(TraditionalForm\`{\((x(1))\) (t), \((x(2))\) (t)}\)], "Output", CellLabel->"Out[12]="] }, Open ]], Cell[CellGroupData[{ Cell["x0", "Input", CellLabel->"In[13]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[13]="] }, Open ]], Cell[CellGroupData[{ Cell["b", "Input", CellLabel->"In[14]:="], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell["a", "Input", CellLabel->"In[15]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"0", \(-1\)}, {"1", "0"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[15]="] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ansdsolve=DSolve[{ 1+ - x2[t] - x1'[t]==0, 4+ 1*x1[t] - x2'[t]==0, x1[0]==1,x2[0]==-3 }, {x1[t], x2[t]}, t]\ \>", "Input", CellLabel->"In[16]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] 5\ \(cos(t)\) + 4\ \(sin(t)\) - 4, x2(t) \[Rule] \(-4\)\ \(cos(t)\) + 5\ \(sin(t)\) + 1}}\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ Cell["FullSimplify[ansdsolve]", "Input", CellLabel->"In[17]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] 5\ \(cos(t)\) + 4\ \(sin(t)\) - 4, x2(t) \[Rule] \(-4\)\ \(cos(t)\) + 5\ \(sin(t)\) + 1}}\)], "Output", CellLabel->"Out[17]="] }, Open ]], Cell["Which matches the answer obtained from the expansion. ", "Text"], Cell[CellGroupData[{ Cell["ExpToTrig[ansfinal]", "Input", CellLabel->"In[18]:="], Cell[BoxData[ \(TraditionalForm \`{5\ \(cos(t)\) + 4\ \(sin(t)\) - 4, \(-4\)\ \(cos(t)\) + 5\ \(sin(t)\) + 1}\)], "Output", CellLabel->"Out[18]="] }, Open ]], Cell["\<\ We see that although there are two eigenvalues, the solution of \ both variables exhibits the same behavior. \ \>", "Text"], Cell[CellGroupData[{ Cell["Plot[{x1[t]/.ansdsolve,x2[t]/.ansdsolve},{t,0,10}]", "Input", CellLabel->"In[19]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.358601 0.0330562 [ [.21429 .3461 -3 -9 ] [.21429 .3461 3 0 ] [.40476 .3461 -3 -9 ] [.40476 .3461 3 0 ] [.59524 .3461 -3 -9 ] 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", "Text"], Cell[CellGroupData[{ Cell["b={0,0,0}", "Input", CellLabel->"In[42]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`{0, 0, 0}\)], "Output", CellLabel->"Out[42]="] }, Open ]] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,-3,1}", "Input", CellLabel->"In[43]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\), 1}\)], "Output", CellLabel->"Out[43]="] }, Open ]], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[44]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-0.476487490321177364`\), \(-0.685875234083421769`\), \(-0.550031667123300671`\)}, {"0.463158454700732935`", "0.534349881187747932`", \(-0.707074571961026343`\)}, {\(-0.353601265449103374`\), "0.902796627438581644`", \(-0.244794596668953445`\)} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[44]="] }, Open ]], Cell[CellGroupData[{ Cell["evals=Eigenvalues[a]", "Input", CellLabel->"In[45]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{10.804959344803613`, \(-5.85240145608776973`\), 0.0474421112841687975`} \)], "Output", CellLabel->"Out[45]="] }, Open ]], Cell["Here is the form of the answer.", "Text"], Cell[CellGroupData[{ Cell["\<\ ans=Sum[c[i] Exp[evals[[i]] t] evs[[i]],{i,1,Length[a]}] - \ Inverse[a].b\ \>", "Input", CellLabel->"In[46]:="], Cell[BoxData[ \(TraditionalForm \`{\(-0.476487490321177364`\)\ \[ExponentialE]\^\(10.804959344803613`\ t\)\ \(c(1)\) + 0.463158454700732935`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\)\ \(c(2)\) - 0.353601265449103374`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\)\ \(c(3)\) + 0.`, \(-0.685875234083421769`\)\ \[ExponentialE]\^\(10.804959344803613`\ t\)\ \(c(1)\) + 0.534349881187747932`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\)\ \(c(2)\) + 0.902796627438581644`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\)\ \(c(3)\) + 0.`, \(-0.550031667123300671`\)\ \[ExponentialE]\^\(10.804959344803613`\ t\)\ \(c(1)\) - 0.707074571961026343`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\)\ \(c(2)\) - 0.244794596668953445`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\)\ \(c(3)\) + 0.`}\)], "Output", CellLabel->"Out[46]="] }, Open ]], Cell["\<\ Now all that remains is to evaluate the constants using the initial \ conditions\ \>", "Text"], Cell[CellGroupData[{ Cell["ans2=(ans/.t->0)-x0", "Input", CellLabel->"In[47]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{\(-0.476487490321177364`\)\ \(c(1)\) + 0.463158454700732935`\ \(c(2)\) - 0.353601265449103374`\ \(c(3)\) - 1.`, \(-0.685875234083421769`\)\ \(c(1)\) + 0.534349881187747932`\ \(c(2)\) + 0.902796627438581644`\ \(c(3)\) + 3.`, \(-0.550031667123300671`\)\ \(c(1)\) - 0.707074571961026343`\ \(c(2)\) - 0.244794596668953445`\ \(c(3)\) - 1.`}\)], "Output", CellLabel->"Out[47]="] }, Open ]], Cell["\<\ Now we form the inner product of the above expressions which are \ equations that individually equal 0. \ \>", "Text"], Cell[CellGroupData[{ Cell["evsad=Eigenvectors[Transpose[a]]", "Input", CellLabel->"In[48]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"0.582874404628400899`", "0.417342128411069968`", "0.697196511955133679`"}, {\(-0.700370200142009924`\), \(-0.0820570355889010905`\), "0.709047407204485136`"}, {\(-0.794650649013677767`\), "0.603648354642688467`", \(-0.0643351378277489516`\)} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[48]="] }, Open ]], Cell["Now form the inner product", "Text"], Cell[CellGroupData[{ Cell["ans3=evsad.ans2", "Input", CellLabel->"In[49]:="], Cell[BoxData[ \(TraditionalForm \`{0.582874404628400899`\ \((\(-0.476487490321177364`\)\ \(c(1)\) + 0.463158454700732935`\ \(c(2)\) - 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0.244794596668953445`\ \(c(3)\) - 1.`)\) + 0.603648354642688467`\ \((\(-0.685875234083421769`\)\ \(c(1)\) + 0.534349881187747932`\ \(c(2)\) + 0.902796627438581644`\ \(c(3)\) + 3.`)\)}\)], "Output", CellLabel->"Out[49]="] }, Open ]], Cell["Now solve these", "Text"], Cell[CellGroupData[{ Cell["\<\ ansend=Solve[ans3==Table[0,{j,1,Length[a]}],Table[c[i],{i,1,Length[\ a]}]]\ \>", "Input", CellLabel->"In[50]:="], Cell[BoxData[ \(TraditionalForm \`{{c(1) \[Rule] \(-0.0295997885393785509`\), c(2) \[Rule] \(-0.2930709363612916`\), c(3) \[Rule] \(-3.17203150170590131`\)}}\)], "Output", CellLabel->"Out[50]="] }, Open ]], Cell["Here is the answer", "Text"], Cell[CellGroupData[{ Cell["ansfinal=ans/.ansend[[1]]", "Input", CellLabel->"In[51]:="], Cell[BoxData[ \(TraditionalForm \`{\(0.`\[InvisibleSpace]\) - 0.135738282002792676`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\) + 1.12163435304762648`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\) + 0.0141039289551660367`\ \[ExponentialE]\^\(10.804959344803613`\ t\), \(0.`\[InvisibleSpace]\) - 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x1'[t]==0, 2*x1[t] +3 x2[t] +8 x3[t]- x2'[t]==0, 7*x1[t] +3 x2[t] +1 x3[t]- x3'[t]==0, x1[0]==1,x2[0]==-3,x3[0]==1 }, {x1[t], x2[t],x3[t]}, t]\ \>", "Input", CellLabel->"In[55]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] \((\(-\(\((288225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \))\)/\(( \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\)\)\) + \((134505\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)) \)/\((\(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + \(( 134505\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)) \)/\((\(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) - \(( 62769\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)) \)/\((\(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) - \(( 54900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + \(( 25620\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + \(( 25620\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) - \(( 11956\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + \(( 13725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) - \(( 6405\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) - \(( 6405\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + \(( 2989\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) - 1575\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + 735\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) - 75\/68\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + 35\/68\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + 75\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) - 35\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + 735\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) - 343\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + 35\/68\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) - 49\/204\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) - 35\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + 49\/816\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) - 4725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) - 900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) + 225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) + 2205\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) + 420\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) - 105\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) + 2205\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) + 420\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) - 105\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) - 1029\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) - 196\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\) + 49\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\)) \) - \(( 61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\))\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)) \))\), x2(t) \[Rule] \((2\ \(( \((370575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - \((172935\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - \((172935\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((80703\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((13725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - \((6405\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - \((6405\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + \((2989\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + 2025\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - 945\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + 75\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - 35\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - 945\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + 441\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) - 35\/272\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + 49\/816\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3) \)\^2)\))\) + 6075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) + 225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) - 2835\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) - 105\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) - 2835\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) - 105\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) + 1323\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\) + 49\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\))\)/ \((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)) \))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)) \))\)/ \((816\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\))\))\))\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)) \))\), x3(t) \[Rule] \((61\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\)\ \((39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2)\))\)/ \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + 1\/816\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\)\ \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((\(18 + 46\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\/\(\(- \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\) + Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) - \((\((39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2)\)) \) + \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\)\ \((1 + \(( \((9 + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)) \)/\((408\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2))\))\) - \((61\ \(( 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) \)\^2 - 39\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2 \ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \) - 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 - 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\^2) \))\)/\(( \((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)) \)\ \(( \(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\) + \((\((\(-15\) + 7\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)) \)\ \(( 39 + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\) + 9\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\) + 23\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\))\)\ \((Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1) - Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3))\))\)/ \((816\ \(( 153 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2) \)\^2 + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\) + \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 - 63\ #1 + 3&, 3)\)\^2) \))\))\)}}\)], "Output", CellLabel->"Out[55]="] }, Closed]], Cell[CellGroupData[{ Cell["testplot=Chop[ExpandAll[N[ansdsolve]]]", "Input", CellLabel->"In[56]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] \(-0.135738282002792853`\)\ 2.71828182845904509`\^\(\(-5.85240145608776884`\)\ t\) + 1.12163435304762648`\ 2.71828182845904509`\^\(0.0474421112841681935`\ t\) + 0.0141039289551663582`\ 2.71828182845904509`\^\(10.8049593448036018`\ t\), x2(t) \[Rule] \(-0.156602420024238542`\)\ 2.71828182845904509`\^\(\(-5.85240145608776884`\)\ t\) - 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", "Text"], Cell[CellGroupData[{ Cell["ansfinal", "Input", CellLabel->"In[57]:="], Cell[BoxData[ \(TraditionalForm \`{\(0.`\[InvisibleSpace]\) - 0.135738282002792676`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\) + 1.12163435304762648`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\) + 0.0141039289551660367`\ \[ExponentialE]\^\(10.804959344803613`\ t\), \(0.`\[InvisibleSpace]\) - 0.156602420024238213`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\) - 2.86369934186902685`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\) + 0.0203017618932660504`\ \[ExponentialE]\^\(10.804959344803613`\ t\), \(0.`\[InvisibleSpace]\) + 0.207223006881877447`\ \[ExponentialE]\^\(\(-5.85240145608776973`\)\ t\) + 0.776496172081310831`\ \[ExponentialE]\^\(0.0474421112841687975`\ t\) + 0.0162808210368115542`\ \[ExponentialE]\^\(10.804959344803613`\ t\)} \)], "Output", CellLabel->"Out[57]="] }, Open ]], Cell[CellGroupData[{ Cell["evals", "Input", CellLabel->"In[58]:="], Cell[BoxData[ \(TraditionalForm \`{10.804959344803613`, \(-5.85240145608776973`\), 0.0474421112841687975`} \)], "Output", CellLabel->"Out[58]="] }, Open ]], Cell["\<\ Note that although the eigenvalues are complex and solution \ eigenvectors are also complex, the values of x obtained by integrating a real \ matrix are real. \ \>", "Text"], Cell[CellGroupData[{ Cell["\<\ Chop[Table[{x1[t]/.testplot,x2[t]/.testplot,x3[t]/.testplot},{t,0,5}\ ]]\ \>", "Input", CellLabel->"In[59]:="], Cell[BoxData[ FormBox[ InterpretationBox[ RowBox[{"(", GridBox[{ {\({1.`}\), \({\(-3.`\)}\), \({1.00000000000000022`}\)}, {\({695.998973573806534`}\), \({997.153190615128082`}\), \({802.881586848925543`}\)}, {\({3.42301315810133655`*^7}\), \({4.92722214990545381`*^7}\), \({3.95134320423458262`*^7}\)}, {\({1.68633080506690973`*^12}\), \({2.42737230076129373`*^12}\), \({1.94661006400574692`*^12}\)}, {\({8.30762709701692791`*^16}\), \({1.19583321610469006`*^17}\), \({9.58988026932432724`*^16}\)}, {\({4.09271228253488494`*^21}\), \({5.8912144638416084`*^21}\), \({4.72440810209161643`*^21}\)} }], ")"}], MatrixForm[ {{{1.0}, {-3.0}, {1.0000000000000002}}, {{ 695.99897357380655}, {997.15319061512821}, {802.88158684892551}}, {{ 34230131.581013367}, {49272221.499054536}, {39513432.042345829}}, {{ 1686330805066.9097}, {2427372300761.2935}, {1946610064005.7471}}, {{ 83076270970169280.0}, {1.1958332161046902*^+17}, { 95898802693243264.0}}, {{4.0927122825348855*^+21}, { 5.8912144638416079*^+21}, {4.7244081020916162*^+21}}}, TableDepth -> 2]], TraditionalForm]], "Output", CellLabel->"Out[59]="] }, Open ]], Cell["We can plot the answers. 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", "Text"], Cell[CellGroupData[{ Cell["b={1,4,-3}", "Input", CellLabel->"In[36]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm\`{1, 4, \(-3\)}\)], "Output", CellLabel->"Out[36]="] }, Open ]] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,-3,1}", "Input", CellLabel->"In[37]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\), 1}\)], "Output", CellLabel->"Out[37]="] }, Open ]], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[38]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ { \(\(0.508024880479146645`\[InvisibleSpace]\) + 0.0962169205024596152`\ \[ImaginaryI]\), \(\(0.75651221141959617`\[InvisibleSpace]\) + 0.`\ \[ImaginaryI]\), \(\(-0.250327304599812672`\) + 0.312535661274032516`\ \[ImaginaryI]\)}, { \(\(0.508024880479146645`\[InvisibleSpace]\) - 0.0962169205024596152`\ \[ImaginaryI]\), \(\(0.75651221141959617`\[InvisibleSpace]\) + 0.`\ \[ImaginaryI]\), \(\(-0.250327304599812672`\) - 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6.26414555016702401`*^-45\ \[ImaginaryI]}}\)], "Output", CellLabel->"Out[44]="] }, Open ]], Cell["Here is the answer", "Text"], Cell[CellGroupData[{ Cell["ansfinal=ans/.ansend[[1]]", "Input", CellLabel->"In[45]:="], Cell[BoxData[ \(TraditionalForm \`{\(-1.95999999999999907`\) - \((\(4.47817742671408147`\[InvisibleSpace]\) + 2.50306713426621696`*^-45\ \[ImaginaryI])\)\ \[ExponentialE]\^\(1.60820291053572201`\ t\) + \((\(3.71908871335704382`\[InvisibleSpace]\) - 0.479377075549420883`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) - 3.55938620758584622`\ \[ImaginaryI])\)\ t\) + \((\(3.71908871335704382`\[InvisibleSpace]\) + 0.479377075549420883`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) + 3.55938620758584622`\ \[ImaginaryI])\)\ t\), \(-4.0799999999999974`\) - \((\(9.87385361213332224`\[InvisibleSpace]\) + 5.51896812253407453`*^-45\ \[ImaginaryI])\)\ \[ExponentialE]\^\(1.60820291053572201`\ t\) + \((\(5.47692680606666471`\[InvisibleSpace]\) + 0.323445614345457332`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) - 3.55938620758584622`\ \[ImaginaryI])\)\ t\) + \((\(5.47692680606666471`\[InvisibleSpace]\) - 0.323445614345457332`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) + 3.55938620758584622`\ \[ImaginaryI])\)\ t\), \(1.51999999999999868`\[InvisibleSpace]\) + \((\(2.83734444657396558`\[InvisibleSpace]\) + 1.58592725479019041`*^-45\ \[ImaginaryI])\)\ \[ExponentialE]\^\(1.60820291053572201`\ t\) - \((\(1.67867222328698346`\[InvisibleSpace]\) + 2.36969368484249676`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) - 3.55938620758584622`\ \[ImaginaryI])\)\ t\) - \((\(1.67867222328698346`\[InvisibleSpace]\) - 2.36969368484249676`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) + 3.55938620758584622`\ \[ImaginaryI])\)\ t\)}\)], "Output", CellLabel->"Out[45]="] }, Open ]], Cell["Check this with the built-in function", "Text"], Cell[CellGroupData[{ Cell["Table[x[i][t],{i,1,Length[a]}]", "Input", CellLabel->"In[46]:="], Cell[BoxData[ \(TraditionalForm\`{\((x(1))\) (t), \((x(2))\) (t), \((x(3))\) (t)}\)], "Output", CellLabel->"Out[46]="] }, Open ]], Cell[CellGroupData[{ Cell["x0", "Input", CellLabel->"In[47]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\), 1}\)], "Output", CellLabel->"Out[47]="] }, Open ]], Cell[CellGroupData[{ Cell["b", "Input", CellLabel->"In[48]:="], Cell[BoxData[ \(TraditionalForm\`{1, 4, \(-3\)}\)], "Output", CellLabel->"Out[48]="] }, Open ]], Cell[CellGroupData[{ Cell["a", "Input", CellLabel->"In[49]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ { StyleBox["1.`", StyleBoxAutoDelete->True, PrintPrecision->1], StyleBox["2.`", StyleBoxAutoDelete->True, PrintPrecision->1], StyleBox["6.`", StyleBoxAutoDelete->True, PrintPrecision->1]}, { StyleBox["2.`", StyleBoxAutoDelete->True, PrintPrecision->1], StyleBox["3.`", StyleBoxAutoDelete->True, PrintPrecision->1], StyleBox["8.`", StyleBoxAutoDelete->True, PrintPrecision->1]}, { RowBox[{"-", StyleBox["7.`", StyleBoxAutoDelete->True, PrintPrecision->1]}], StyleBox["3.`", StyleBoxAutoDelete->True, PrintPrecision->1], StyleBox["1.`", StyleBoxAutoDelete->True, PrintPrecision->1]} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[49]="] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ansdsolve=DSolve[{ 1 + x1[t] + 2*x2[t]+6 x3[t] - Derivative[1][x1][t]==0, 4+ 2*x1[t] +3 x2[t] +8 x3[t]- Derivative[1][x2][t]==0, -3- 7*x1[t] +3 x2[t] +1 x3[t]- Derivative[1][x3][t]==0, x1[0]==1,x2[0]==-3,x3[0]==1 }, {x1[t], x2[t],x3[t]}, t]\ \>", "Input", CellLabel->"In[50]:=", AspectRatioFixed->True], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] \((477225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\) - 477225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\) - 525\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2 + 525\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2 - 477225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 477225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 90900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 90900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 3234\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 100\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 3423\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 1386\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 525\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 525\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 3234\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 + 100\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 3423\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 + 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 462\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 + 1386\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3 + 462\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3 + 477225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 477225\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 90900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 90900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 3234\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 3423\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 100\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 1386\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 90900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 90900\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 652\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 652\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 3234\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 3423\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 100\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 652\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 652\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 1386\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 525\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 525\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 3234\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 100\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 3423\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 462\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 3234\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 3423\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 100\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 652\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 652\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 462\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 1386\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 - 462\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 1386\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 - 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 462\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3)\)/ \((352\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2))\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3))\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3))\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\))\), x2(t) \[Rule] \((659025\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\) - 659025\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\) - 725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2 + 725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2 - 659025\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 659025\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 4466\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 4727\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 1914\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 4466\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 4727\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 638\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 + 1914\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3 + 638\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3 + 659025\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 659025\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 4466\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 4727\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 1914\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 22725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 4466\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 4727\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 22\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 1914\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 22\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 725\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 4466\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 4727\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 638\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 4466\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 4727\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 25\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 163\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 22\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 638\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 22\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 1914\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 - 638\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 1914\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 22\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 638\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 - 22\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3)\)/ \((176\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2))\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3))\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3))\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\))\), x3(t) \[Rule] \(-\(\((613575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\) - 613575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\) - 675\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2 + 675\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2 - 613575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 613575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 159075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 159075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 4158\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 175\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 4401\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) - 1782\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\) + 675\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 675\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 4158\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 175\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 4401\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 - 594\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2 + 1782\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3 + 594\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3 + 613575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 613575\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 159075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 159075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 4158\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 4401\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 175\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 1782\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 159075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 159075\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 1141\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 1141\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 4158\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 4401\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 175\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 1141\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 1141\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) + 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 1782\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\) - 675\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 675\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 4158\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 175\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 4401\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 594\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 4158\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 4401\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 175\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 1141\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 1141\ \[ExponentialE]\^\(t\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 594\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 + 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^3\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^2 - 1782\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 - 594\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 1782\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 + 594\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3 - 154\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\^2\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\)\^3)\)/ \((352\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1)\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2))\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2)\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 1) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3))\)\ \((Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 2) - Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3))\)\ \(Root(#1\^3 - 5\ #1\^2 + 21\ #1 - 25&, 3)\))\)\)\)}}\)], "Output", CellLabel->"Out[50]="] }, Closed]], Cell[CellGroupData[{ Cell["testplot=Chop[ExpandAll[N[ansdsolve]]]", "Input", CellLabel->"In[51]:="], Cell[BoxData[ \(TraditionalForm \`{{x1(t) \[Rule] \(-1.95999999999999978`\) - 4.4781774267140797`\ 2.71828182845904509`\^\(1.60820291053572006`\ t\) + \((\(3.71908871335703938`\[InvisibleSpace]\) - 0.479377075549424525`\ \[ImaginaryI])\)\ 2.71828182845904509` \^\(\((\(1.69589854473213996`\[InvisibleSpace]\) - 3.55938620758584889`\ \[ImaginaryI])\)\ t\) + \((\(3.71908871335704027`\[InvisibleSpace]\) + 0.479377075549423636`\ \[ImaginaryI])\)\ 2.71828182845904509` \^\(\((\(1.69589854473213996`\[InvisibleSpace]\) + 3.55938620758584889`\ \[ImaginaryI])\)\ t\), x2(t) \[Rule] \(-4.08000000000000007`\) - 9.8738536121333027`\ 2.71828182845904509`\^\(1.60820291053572006`\ t\) + \((\(5.47692680606665138`\[InvisibleSpace]\) + 0.323445614345449161`\ \[ImaginaryI])\)\ 2.71828182845904509` \^\(\((\(1.69589854473213996`\[InvisibleSpace]\) - 3.55938620758584889`\ \[ImaginaryI])\)\ t\) + \((\(5.47692680606665138`\[InvisibleSpace]\) - 0.323445614345450316`\ \[ImaginaryI])\)\ 2.71828182845904509` \^\(\((\(1.69589854473213996`\[InvisibleSpace]\) + 3.55938620758584889`\ \[ImaginaryI])\)\ t\), x3(t) \[Rule] \(1.52000000000000001`\[InvisibleSpace]\) + 2.83734444657395776`\ 2.71828182845904509`\^\(1.60820291053572006`\ t\) - \((\(1.67867222328697884`\[InvisibleSpace]\) + 2.36969368484248965`\ \[ImaginaryI])\)\ 2.71828182845904509` \^\(\((\(1.69589854473213996`\[InvisibleSpace]\) - 3.55938620758584889`\ \[ImaginaryI])\)\ t\) - \((\(1.6786722232869784`\[InvisibleSpace]\) - 2.36969368484248965`\ \[ImaginaryI])\)\ 2.71828182845904509` \^\(\((\(1.69589854473213996`\[InvisibleSpace]\) + 3.55938620758584889`\ \[ImaginaryI])\)\ t\)}}\)], "Output", CellLabel->"Out[51]="] }, Open ]], Cell["Which matches the answer obtained from the expansion. ", "Text"], Cell[CellGroupData[{ Cell["ansfinal", "Input", CellLabel->"In[52]:="], Cell[BoxData[ \(TraditionalForm \`{\(-1.95999999999999907`\) - \((\(4.47817742671408147`\[InvisibleSpace]\) + 2.50306713426621696`*^-45\ \[ImaginaryI])\)\ \[ExponentialE]\^\(1.60820291053572201`\ t\) + \((\(3.71908871335704382`\[InvisibleSpace]\) - 0.479377075549420883`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) - 3.55938620758584622`\ \[ImaginaryI])\)\ t\) + \((\(3.71908871335704382`\[InvisibleSpace]\) + 0.479377075549420883`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) + 3.55938620758584622`\ \[ImaginaryI])\)\ t\), \(-4.0799999999999974`\) - \((\(9.87385361213332224`\[InvisibleSpace]\) + 5.51896812253407453`*^-45\ \[ImaginaryI])\)\ \[ExponentialE]\^\(1.60820291053572201`\ t\) + \((\(5.47692680606666471`\[InvisibleSpace]\) + 0.323445614345457332`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) - 3.55938620758584622`\ \[ImaginaryI])\)\ t\) + \((\(5.47692680606666471`\[InvisibleSpace]\) - 0.323445614345457332`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) + 3.55938620758584622`\ \[ImaginaryI])\)\ t\), \(1.51999999999999868`\[InvisibleSpace]\) + \((\(2.83734444657396558`\[InvisibleSpace]\) + 1.58592725479019041`*^-45\ \[ImaginaryI])\)\ \[ExponentialE]\^\(1.60820291053572201`\ t\) - \((\(1.67867222328698346`\[InvisibleSpace]\) + 2.36969368484249676`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) - 3.55938620758584622`\ \[ImaginaryI])\)\ t\) - \((\(1.67867222328698346`\[InvisibleSpace]\) - 2.36969368484249676`\ \[ImaginaryI])\)\ \[ExponentialE]\^\(\(( \(1.69589854473213774`\[InvisibleSpace]\) + 3.55938620758584622`\ \[ImaginaryI])\)\ t\)}\)], "Output", CellLabel->"Out[52]="] }, Open ]], Cell[CellGroupData[{ Cell["evals", "Input", CellLabel->"In[59]:="], 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", "Text"], Cell[CellGroupData[{ Cell["a={{1,3},{3,1}}", "Input", CellLabel->"In[61]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3"}, {"3", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[61]="] }, Open ]], Cell[CellGroupData[{ Cell["b={1,4}", "Input", CellLabel->"In[62]:="], Cell[BoxData[ \(TraditionalForm\`{1, 4}\)], "Output", CellLabel->"Out[62]="] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,-3}", "Input", CellLabel->"In[63]:="], Cell[BoxData[ \(TraditionalForm\`{1, \(-3\)}\)], "Output", CellLabel->"Out[63]="] }, Open ]], Cell[TextData[{ "if the original problem is, ", Cell[BoxData[ \(TraditionalForm\`dy\/dt\)]], "=", Cell[BoxData[ \(TraditionalForm\`\(\ A\ y\ \)\)]], ", then we can use the eigenvectors of ", Cell[BoxData[ \(TraditionalForm\`A\)]], " to do a linear transformation that will make the original matrix \ diagonal (if there are no repreated roots.) For y = T z, then T ", Cell[BoxData[ \(TraditionalForm\`dy\/dt\)]], "=", Cell[BoxData[ \(TraditionalForm\`\(\ A\ T\ z\ \ \)\)]], "or ", Cell[BoxData[ \(TraditionalForm\`dz\/dt\)]], "=", Cell[BoxData[ \(TraditionalForm\`\(\ \((T\^\(-1\)\ A\ T\ )\) z\ \)\)]], ". " }], "Text"], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[64]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-1\), "1"}, {"1", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[64]="] }, Open ]], Cell[CellGroupData[{ Cell["tt=Transpose[evs]", "Input", CellLabel->"In[65]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-1\), "1"}, {"1", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[65]="] }, Open ]], Cell[CellGroupData[{ Cell["ttinv=Inverse[tt]", "Input", CellLabel->"In[66]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-\(1\/2\)\), \(1\/2\)}, {\(1\/2\), \(1\/2\)} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[66]="] }, Open ]], Cell["OK, let's see if it works,", "Text"], Cell[CellGroupData[{ Cell["diag1=ttinv.a.tt", "Input", CellLabel->"In[67]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-2\), "0"}, {"0", "4"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[67]="] }, Open ]], Cell["The initial condition is", "Text"], Cell[CellGroupData[{ Cell["initial =ttinv.x0", "Input", CellLabel->"In[68]:="], Cell[BoxData[ \(TraditionalForm\`{\(-2\), \(-1\)}\)], "Output", CellLabel->"Out[68]="] }, Open ]], Cell[CellGroupData[{ Cell["ttinv.b", "Input", CellLabel->"In[69]:="], Cell[BoxData[ \(TraditionalForm\`{3\/2, 5\/2}\)], "Output", CellLabel->"Out[69]="] }, Open ]], Cell["Thus we can solve:", "Text"], Cell[CellGroupData[{ Cell["\<\ ansx=DSolve[{3/2-2 z1[t]-z1'[t]==0,5/2+4 z2[t]-z2'[t]==0,z1[0]==-2, z2[0]==-1},{z1[t],z2[t]},t]\ \>", "Input", CellLabel->"In[70]:="], Cell[BoxData[ FormBox[ RowBox[{ \(General::"spell1"\), \( : \ \), "\<\"Possible spelling error: new symbol name \ \\\"\\!\\(TraditionalForm\\`ansx\\)\\\" is similar to existing symbol \\\"\\!\ \\(TraditionalForm\\`ans\\)\\\".\"\>"}], TraditionalForm]], "Message"], Cell[BoxData[ 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", "Text"], Cell[CellGroupData[{ Cell["a={{1,3},{3,1}}", "Input", CellLabel->"In[81]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {"1", "3"}, {"3", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[81]="] }, Open ]], Cell[CellGroupData[{ Cell["b={0,0}", "Input", CellLabel->"In[82]:="], Cell[BoxData[ \(TraditionalForm\`{0, 0}\)], "Output", CellLabel->"Out[82]="] }, Open ]], Cell["Here is the initial condition @ t=0.", "Text"], Cell[CellGroupData[{ Cell["x0={1,2}", "Input", CellLabel->"In[92]:="], Cell[BoxData[ \(TraditionalForm\`{1, 2}\)], "Output", CellLabel->"Out[92]="] }, Open ]], Cell[TextData[{ "if the original problem is, ", Cell[BoxData[ \(TraditionalForm\`dy\/dt\)]], "=", Cell[BoxData[ \(TraditionalForm\`\(\ A\ y\ \)\)]], ", then we can use the eigenvectors of ", Cell[BoxData[ \(TraditionalForm\`A\)]], " to do a linear transformation that will make the original matrix \ diagonal (if there are no repreated roots.) For y = T z, then T ", Cell[BoxData[ \(TraditionalForm\`dy\/dt\)]], "=", Cell[BoxData[ \(TraditionalForm\`\(\ A\ T\ z\ \ \)\)]], "or ", Cell[BoxData[ \(TraditionalForm\`dz\/dt\)]], "=", Cell[BoxData[ \(TraditionalForm\`\(\ \((T\^\(-1\)\ A\ T\ )\) z\ \)\)]], ". " }], "Text"], Cell[CellGroupData[{ Cell["evs=Eigenvectors[a]", "Input", CellLabel->"In[84]:=", AspectRatioFixed->True], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-1\), "1"}, {"1", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[84]="] }, Open ]], Cell[CellGroupData[{ Cell["tt=Transpose[evs]", "Input", CellLabel->"In[85]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-1\), "1"}, {"1", "1"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[85]="] }, Open ]], Cell[CellGroupData[{ Cell["ttinv=Inverse[tt]", "Input", CellLabel->"In[86]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-\(1\/2\)\), \(1\/2\)}, {\(1\/2\), \(1\/2\)} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[86]="] }, Open ]], Cell["OK, let's see if it works,", "Text"], Cell[CellGroupData[{ Cell["diag1=ttinv.a.tt", "Input", CellLabel->"In[87]:="], Cell[BoxData[ FormBox[ RowBox[{"(", GridBox[{ {\(-2\), "0"}, {"0", "4"} }, ColumnAlignments->{Decimal}], ")"}], TraditionalForm]], "Output", CellLabel->"Out[87]="] }, Open ]], Cell["The initial condition is", "Text"], Cell[CellGroupData[{ Cell["initial =ttinv.x0", "Input", CellLabel->"In[93]:="], Cell[BoxData[ \(TraditionalForm\`{1\/2, 3\/2}\)], "Output", CellLabel->"Out[93]="] }, Open ]], Cell[CellGroupData[{ Cell["ttinv.b", "Input", CellLabel->"In[89]:="], Cell[BoxData[ \(TraditionalForm\`{0, 0}\)], "Output", CellLabel->"Out[89]="] }, Open ]], Cell["Thus we can solve:", "Text"], Cell[CellGroupData[{ Cell["\<\ ansx=DSolve[{ -2 z1[t]-z1'[t]==0, 4 z2[t]-z2'[t]==0,z1[0]==1/2, z2[0]==3/2},{z1[t],z2[t]},t]\ \>", "Input", CellLabel->"In[94]:="], Cell[BoxData[ \(TraditionalForm \`{{z1(t) \[Rule] \[ExponentialE]\^\(\(-2\)\ t\)\/2, z2(t) \[Rule] \(3\ \[ExponentialE]\^\(4\ t\)\)\/2}}\)], "Output", CellLabel->"Out[94]="] }, Open ]], Cell["\<\ Now one of the modes decays to 0 while the other one exhibits the \ behavior of largest eigenvalue. 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