Hi,

I have to solve a boundary value problem that involves finding function

that is harmonic on an annulus centered at

in the plane and takes the value zero on the inner boundary (radius 1) and ten on the outer (radius 2.) Once in possession of this function, I have to evaluate it at (0,0). The solutions I was given don't give the function but just the value of phi (1/2.) I'm not getting this answer; I tried setting up a system of equations with the solution form

but kept getting

I'd appreciate at least an understanding of why their answer is right. Also, the solution should involve elementary methods (no crazy transforms please.) Thanks!