I have looked all over the place and it seems I can't find a reference for solution methods to common forms of first order nonlinear ordinary differential equations (ODEs). Currently, I am starting at the following population model
$$ \dot P = a P^2 - b P $$
given $a, b > 0$, and not really getting anywhere with this. It seems that Wolfram|Alpha cannot parse it so I can't search the solution steps for insight, though maybe there's some special syntax I should be using there.
How would I go about solving this one in particular, and where would I find a compendium of ODE solution methods?