HELP!!: Laplace 2D equation on a square

[SarahRoberts]

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....

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

I do the usual thing of seperating varibales on

which leads to the equations:

so i solved these equations and applyed the boundary conditions:

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

this gives the equation

but then if i sub in the non-homogenous BC,

i get 0 = x

lol, what have i done this time!

any help would be so very much appreciated!

Cheers
Sarah