Solve uxx + uyy = -g(y) with 0 < x < infinity, 0 < y < pi

with the following boundary conditions:

(i) u(0,y) = 0

(ii) lim as x goes to infinity of (x,y) exists and is finite

(iii) u(x,0) = 0

(iv) u(x,pi) = 0

I have this hint: Assume a solution of the form u(x,y) = summation (n=1 to infinity) of Bn(x)sin(ny)

How can I solve this and what does this describe physically?