Stability of equilibrium point for an autonomous system of first order ODE

Question

I'm dealing with the following problem. Determine whether the equilibrium point (0,0) of the following ODE is stable or not. \begin{cases} \dot x = xy + x^3, \\ \dot y = -y -2x^2. \end{cases} The stability of a equilibrium point is in the liapunov sense, i.e. for any neighborhood $U(x_0)$ of the equilibrium point $x_0$, there exists a $V(x_0)$ contained in $U(x_0)$, s.t. any trajectories starting from $V(x_0)$ is contained in $U(x_0)$. I guess it could be worked out by constructing some liapunov function but I cannot figure it out now.