This question is confusing me because there are 2 sets of boundary conditions. I don't understand if I'm supposed to solve for $u_{xx} + u_{yy} = 0$ or $v_{xx} +v_{yy} = 0$. From the question, it seems like it's the latter. But why are the $u$ boundary conditions there? Do I use them at all? And why are they different to the $v$ boundary conditions? I know how to solve Laplace Equations but this one seems a little strange.
In the beginning, am I supposed to try $v(x,y) = X(x)Y(y)$ or $u(x,y) = X(x)Y(y)$?