HELP!!: Laplace 2D equation on a square

Hi everyone,

I quite get the answer out for this question and i just feel like i have been beating my head into a wall for 4 hours! aghh....

http://img167.imageshack.us/img167/3...cture12vv7.png

I get stuck when i try to solve the sub-problem which has boundary conditions:

http://img172.imageshack.us/img172/8...cture13gn5.png

I do the usual thing of seperating varibales on http://img167.imageshack.us/img167/2...cture14eh5.png which leads to the equations:

http://img167.imageshack.us/img167/6...cture15oe2.png

so i solved these equations and applyed the boundary conditions:

X'(0) = 0, X'(1) = 0, Y(1) = 0

this gives the equation http://img147.imageshack.us/img147/634/picture16pd3.png

but then if i sub in the non-homogenous BC, http://img147.imageshack.us/img147/8...cture17zg4.png

i get 0 = x

lol, what have i done this time! :P

any help would be so very much appreciated! :)

Cheers

Sarah