Dirichlet problem for a rectangle

[vams42]

Hello,

am new to the dirichlet topic, and am unable to understand how to solve it, neither the approach to solve the problem. could you tell me how to solve this problem, if so it wil be helpful in solving other problems also

the problem is


solve the following dirichlet problem


(laplace equation) del^2 = 0

0<x<1, 0<y<1

u(x,0) = x(x-1)
u(x,1) = 0
u(0,y) = 0
u(1,y) = 0

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