I came across the following question in one of my professor's past exams:
Find a Lyapunov function for $(0,0)$ in the system: $ \left\{ \begin{array}{ll} \dot{x} = -x -2y + x^2\\ \dot{y} = x - 4y + xy \end{array}\right. $
I know there is no formula for finding Lyapunov functions for a system, so how do I start solving such problems?
Thanks!