I'm having trouble finding the solution to the problem: $u_{xx}+u_{yy}=0$ with the boundary conditions $u(x,1)=-x,u(x,-1)=x,u(1,y)=-y,u(-1,y)=y$. I've been suggested to try separation of variables, and I arrived to a solution that involves sines, cosines and exponentials. The problem is that i can't find a way to assign values to the coefficients, such that the boundary conditions are satisfied. Could you help me with any suggestions?
Thank you!