UsubX = means partial of u with respect to x, for my halfasses notation... so I have x^2*Usubx - Usuby + U = 0, I'm sposed to solve by a variable transformation thingy, and by seperation of variables. Doing the transformation I get U=const*e^(1/x) which is a solution, by my own checking. Yay Now at this point I noted if that's the general solution(which I think that method finds)then there IS no seperated solution, and indeed despite my careful efforts whatever I get using SOV doesn't check out right. So assuming I'm right and didn't just muck it up, is this problem meant to teach us the potential failing of the SOV method? If so is there anyway to tell earlier it won't work besides doing it and checking? And a semi-related question for clarification, if you use SOV(and get a solution that works) the solution is not guaranteed to be the most general solution, rather the most general seperated solution?