help with PDE in circular annulus(poisson eq)

AlephZero

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).

AlephZero $Math 2012$ Recognitions: Science Advisor	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).