Have a look at this Phase
Portrait applet! To visualize the ODE y'=x-y^2, for example,
type
in x'=1 and y'=x-y^2, and click "reset" so that your
new ODE
takes effect. Then go to the "phase portrait" window
and click
on it: a numerical solution will be generated with your clicked
point
as the initial point. (Note: x'=1 makes x the independent
variable.)
Solutions to some modelling problems
can be found here, especially for some who had to miss class Friday.