I see some symmetries in your DE of which we might want to take advantage. For example:

I'm thinking a substitution of the form or might be good to try. If we have , then and

. It follows, then, that the DE becomes

or Therefore,

The resulting DE is separable.

Conversely, if you try then and thus The DE becomes

I don't see how this substitution will help you as much as the other one.