Need help finding a Lyapunov function [closed]

In a sample exam for a course in ordinary differential equations I encountered the following problem:

Prove that the origin is an asymptotically stable equilibrium point of the system x'=-y^3-(3/2)x-(1/6)x^3 y'=-(1/2)y^8

The linearization has eigenvalue 0, so I assume that the main part of the problem is finding a Lyapunov function. I have tried, without success, the simplest forms, like E=ax^2+by^2, and am now stuck... Help would be much appreciated!

-
 This question is really not at a level appropriate to this web site, but: Have you noticed that the equation for y is decoupled from the other one? – Michael Renardy Aug 16 2011 at 12:58 Concerning your first comment: Sorry, I was unaware of that. Thank you for taking your time to help anyway, as it happens what you are pointing out had somehow escaped me! – Daniel Aug 16 2011 at 14:24 try math.stackexchange.com/questions?sort=newest – Will Jagy Aug 16 2011 at 19:18 Thank you! I will use that site for my future questions (at least for a couple of years to come...) Again, sorry for not checking more thoroughly what sort of questions this site is for. – Daniel Aug 16 2011 at 20:23