Hi there, for the following equation that is in the phase plane (x,y),

<--- sorry, there was a typo originally, now correct

where

I need to prove that the solutions of the coupled, nonlinear system are given by

where C is a constant. So what I have done so far is:

So the equivalent system is:

(as stated in the question)

So from this, I tried letting

This upon solving this, I got

which seems close, but I am not sure this is the right method or not