Okay so I've changed the 2nd order nonlinear ODE
$$ x'' = a(x')^2 - ax' -ax $$ where a is a real constant,
into $$ x' = y $$ $$ y' = ay^2 -ay - ax $$
I'm asked to verify the critical point (0,0). Thats easy and done.
The problem is now how to place the transformed system into matrix form so i can determine eigenvalues etc.... How do I work with the term $$ y^2 $$
???
Am I meant to use some other means to classify the critcal point?