Chapter 12.5, Problem 5E

In Problems $1-8$ , use Lyapunov’s direct method to determine the stability of the origin for the given system.

$\begin{array}{l}\frac{dx}{dt}=2x^3,\\ \frac{dy}{dt}=2x^{2}y-y^3\end{array}$

[Hint: Try $V\left(x^2+y^2\right)=x^2-y^2$.]