NiQtSSVtcm93RzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiUtSSNtaUdGJTY5USFGKC8lJ2ZhbWlseUdRK01vbm9zcGFjZWRGKC8lJXNpemVHUSMxMkYoLyUlYm9sZEdRJXRydWVGKC8lJ2l0YWxpY0dGOC8lKnVuZGVybGluZUdRJmZhbHNlRigvJSpzdWJzY3JpcHRHRj0vJSxzdXBlcnNjcmlwdEdGPS8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GKC8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRigvJSdvcGFxdWVHRj0vJStleGVjdXRhYmxlR0Y4LyUpcmVhZG9ubHlHRj0vJSljb21wb3NlZEdGPS8lKmNvbnZlcnRlZEdGPS8lK2ltc2VsZWN0ZWRHRj0vJSxwbGFjZWhvbGRlckdGPS8lMGZvbnRfc3R5bGVfbmFtZUdRLE1hcGxlfklucHV0RigvJSptYXRoY29sb3JHRkQvJS9tYXRoYmFja2dyb3VuZEdGRy8lK2ZvbnRmYW1pbHlHRjIvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRigvJSltYXRoc2l6ZUdGNS1GJDYlLUYtNjlRJXdpdGhGKEYwRjNGNi9GOkY9RjtGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbi9Gam5RJWJvbGRGKEZcby1JI21vR0YlNjNRMCZBcHBseUZ1bmN0aW9uO0YoLyUlZm9ybUdRJmluZml4RigvJSZmZW5jZUdGPS8lKnNlcGFyYXRvckdGPS8lJ2xzcGFjZUdRJDBlbUYoLyUncnNwYWNlR0ZjcC8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobWF4c2l6ZUdRKWluZmluaXR5RigvJShtaW5zaXplR1EiMUYoLyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYoLyUlc2l6ZUdGNS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRigvJStiYWNrZ3JvdW5kR0ZHLUkobWZlbmNlZEdGJTYjLUYkNiMtRi02OVEoREV0b29sc0YoRjBGM0Y2RmNvRjtGPkZARkJGRUZIRkpGTEZORlBGUkZURlZGWUZlbkZnbkZkb0Zcby1GZ282M1EiO0YoRmpvRl1wL0ZgcEY4RmFwL0ZlcFEvdGhpY2ttYXRoc3BhY2VGKEZmcEZocEZqcEZdcUZgcUZicUZkcUZmcUZpcUZbckZecjcjQyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHRio2I0koREV0b29sc0dGYnMiIiI=
Tanya Salyers
University of Notre Dame
Calculus II: Summer 2007
plot([-0.5*x,-1*x,-5*x,0.5*x,1*x,5*x],x=-1..1, legend=["-0.5","-1","-5","0.5","1","5"]);
D1:= diff(x(t),t)=x(t)+t;
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(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);
D2:= diff(y(x),x)=y(x)*sin(x);
DEplot(D2,[y(x)],x=-10..10,[[y(1)=1],[y(1)=-3],[y(1)=3]],stepsize=0.01,title=`y'=x^2+y^2-1`,color=red,linecolor=x/2,arrows=MEDIUM,method=rkf45);
D3:= diff(R(t),t)=k*R(t);
k:=5;
DEplot(D3,[R(t)],t=0..1,[[R(1)=1],[R(1)=-3],[R(1)=3]],stepsize=0.01,title=`Population growth`,color=red,linecolor=t/2,arrows=MEDIUM,method=rkf45);