
The great thing about this diagram is that it shows you how different solution curves act with respect to the given differential equation. To produce this pretty picture you would use the following maple code:
> solve(x^3*(x^2-4),x);
> with (plots):
with(DEtools):
de:=diff(x(t),t)=x^3*(x^2-4);
> with (plots):
with (DEtools):
slopes:=dfieldplot(de,x(t),t=0..3,x=-3..3):
display(slopes);
Exciting isn't it? These things really do represent a great deal of my life right now. If only I could understand the discrete math as well as these, I would be doing great!
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