Slope Field and Solutions to a Differential Equation
 
Maple 8 code:
  
with(DEtools):with(plots):
plotsetup(gif, plotoptions=`transparent=true,
   width=180, height=180`, plotoutput=`slope1.gif`):
P:=dfieldplot(diff(y(x),x)=y(x)+x^2,y(x),
   x=-2..2, y=-2..2, thickness=1):
f:=x->-x^2*exp(-x)-2*x*exp(-x)-2*exp(-x)+1;
g:=x->exp(x)*f(x);
Q1:=animatecurve(g(x),x=-2..2, color=black,
   thickness=2, frames=50, xtickmarks=0, ytickmarks=0):
display({P,Q1});
plotsetup(gif, plotoptions=`transparent=true,
   width=180,height=180`, plotoutput=`slope2.gif`):
R:=plot(g(x), x=-2..2, color=black, thickness=2,
   xtickmarks=0, ytickmarks=0):
g1:=x->exp(x)*(f(x)+1);
Q2:=animatecurve(g1(x),x=-2..2, color=blue,
   thickness=2, frames=50, xtickmarks=0, ytickmarks=0):
display({P,R,Q2});
plotsetup(default):
Comments: 
  1. This is actually two animations that we concatenated in our animation editor.
  2. We lengthened the display time for every frame, and further lengthened the time for the first and last frames, as well as the frame that shows the completed first curve.
  3. The "plotsetup" commands make this animation transparent.  You won't see the plots in the Maple worksheet.  Instead, they will be stored as "slope1.gif" and "slope2.gif" in your Maple directory.