Show that u=f(2x+y^2)+g(2x-y^2) satisfies the equation y^2 d^2u/dx^2 + (1/y) du/dy - d^2u/dy^2=0 where f and g are arbitrary (twice differentiable) functions.

I came up with fxx=0 fyy=2 gxx=0 gyy= 2. I think I need to come up with ux, uy, uxx and uyy but I'm not sure I am coming up with the correct answers. Can someone just show me how to do uxx and I can verify if I am doing it correctly. Thanks!