
stable/unstable DEs
Consider the differential equation given by
$\displaystyle y'=ayb^2y, a>0, b>0$
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:
$\displaystyle y'=y(aby)$
so the solutions are $\displaystyle y=0 , y=a/b$
But how to do I see whether they're stable, unstable, or semi stable?
any help is appreciated, thanks!

I'm not 101% about this but...
Calculate the derivative of $\displaystyle ay  by^2$ and sub in the equilibrium values you found.
If its < 0 they are stable (and in fact, a sink)
If it's > 0 they are unstable (and a source)
If it's = 0 we need more info.