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i let u(x, y) = F(x) G(y)
so
Uxx = F'' G
Uyy = F G"
then the equation become F"G + FG" = 0
i separate the variables and equate them to a separation constant, k
so the 2 2nd order ODE are
F''-kF=0 , G"+kG = 0
how do i proceed with the initial conditions given?

do you have relevant links?

hold on for a while ... I'll work out few other probs and try to work on my copy.

oh kay. thx alot

my lecturer practically skipped this part ==

So why do we choose the coordinates ? - To fit the symmetry of the boundary of course !