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
Tanya Salyers
University of Notre Dame
Calculus II: Summer 2007
D1:= diff(x(t),t)=x(t)+t;
dsolve(D1);dsolve({D1,x(0)=1});s:=t->-1-t+2*exp(t);
DEplot(D1,[x(t)],t=-4..4,[[x(0)=1],[x(0)=-1],[x(1)=-1]],stepsize=0.2,title=`y'=x+y`,color=red,linecolor=t/2,arrows=MEDIUM,method=rkf45);
f:=(t,x)->x+t;
t0:=0;x0:=1;h:=0.1;
x1:=x0+h*f(t0,x0);t1:=t0+h;
s(t1);
x2:=x1+h*f(t1,x1);t2:=t1+h;
s(t2);
x3:=x2+h*f(t2,x2);t3:=t2+h;
s(t3);
x4:=x3+h*f(t3,x3);t4:=t3+h;
s(t4);
l:=t->Spline([[t0,x0],[t1,x1],[t2,x2],[t3,x3]], t, degree=1):
plot([s(t),l(t)],t=0..0.4,legend=["exact","euler"]);
s;
s;
s;