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Dec29-11, 01:28 PM
Sci Advisor
HW Helper
P: 7,284
Using the idea of separating the variables, you should be able to see from the PDE that

A(r,θ) = Cn(r) cos(nθ) + Sn(r) sin(nθ)

is a solution for the right hand side terms (1/r)(Xn cos(nθ) + Yn sin(nθ))

That will give you ordinary differential equations to solve for Cn(r) and Sn(r).