# stable/unstable DEs

• Apr 25th 2010, 01:35 PM
cdlegendary
stable/unstable DEs
Consider the differential equation given by

$y'=ay-b^2y, a>0, b>0$

List the equilibrium solutions in increasing order and classify them as stable, semistable, or unstable.

I think I know to find the equilibrium solutions; you just factor out the y and get:

$y'=y(a-by)$

so the solutions are $y=0 , y=a/b$

But how to do I see whether they're stable, unstable, or semi stable?

any help is appreciated, thanks!
• Apr 25th 2010, 04:43 PM
Calculate the derivative of $ay - by^2$ and sub in the equilibrium values you found.