Very sorry, I've posted the question wrong. My problems remain though...

The actual question should have read:

The conserved quantity is:

Here's what I did with it though, maybe this will help...

If you ignore the 'c'.

Then you can do the following.

so

then multiply through by [tex] y' [\math] to get

then substitute (ignoring c) to get

Which you can integrate to get:

Which gives the result. Don't know how to do it with the c though.