1. The problem statement, all variables and given/known data I'm having issues with a Laplace problem. actually, I have two different boundary problems which I dont know how to solve analytically. I couldn't find anything on this situations and if anybody could point me in the right direction it would be fantastic. It's just Laplace's equation on the square [0,a]x[0,b] with a mixed boundary. 2. Relevant equations the first one is: Uxx+Uyy=0 Ux(0,y)= 0 Ux(a,y)= f(y) (some function) U(x,0)= 0 Uy(x,b)= v (some constant) the second is: Uxx+Uyy=0 Ux(0,y)= 0 U(a,y)= g(y) (some function) U(x,0)= 0 Uy(x,b)= v (some constant) 3. The attempt at a solution I tried to do ordinary separable solution but I don't really know how to do this in such problems.