I have no idea what you're doing there. "Solving for y' "?? "Then v = ... and w = ..."??

The equation you gave mentions one function only, u(x,y). So what's y'? What are v and w? Why do you have complex numbers - is u complex valued, or do they arise in whatever way you went about solving this?

Remember - we can't read your mind. You'll need to give more details before we can even understand the problem.