Construct a Lyapunov Function in order to show that the system \begin{align}\frac{dx}{dt}&=x(y^2 +1) +y \\ \frac{dy}{dt} &= x^2y +x\end{align} has no closed orbits (limit cycle) and hence no periodic solutions.
I have absolutely no experience in constructing Lyapunov functions. Can anyone please help guide me with this? I know the conditions that the Lyapunov function $L(x,y)$ must satisfy, but I do not know how to "create" the function $L$.