I'm presuming you mean partials instead of d's above, otherwise that wouldn't make much sense
Other than that, it's not a very easy equation to solve. It might be possible (I've not done PDEs for a while), but it looks good because the left and right hand sides are independent of each other, so I think you can set the left hand side = right hand side = constant. As I said, I've not done this for a while though and I could be hugely wrong. Also, that doesn't seem to help very much with the RHS, because that's non-linear. woohoo.
My 2 cents worth.