1. The problem statement, all variables and given/known data Solve Laplace's equation [tex] \nabla^2 u(r,\vartheta) =0[/tex] in an annulus with inner radius [tex] r_1 [/tex] and outer radius [tex] r_2 [/tex]. (a) For boundary conditions take [tex] u(1,\vartheta) = 3 [/tex] and [tex] u(2,\vartheta) = 5[/tex]. (b) What is the solution using this second set of boundary conditions [tex] u(1,\vartheta) = cos(\vartheta) [/tex] and [tex] u(2, \vartheta) = sin(\vartheta) [/tex]? 2. Relevant equations 3. The attempt at a solution I's assuming I'm going to get Bessel functions out of this but I don't know what the exact solution is and I'm having an even harder time applying the boundary conditions.