2. Laplace Equation in Polar Coordinates with periodic Boundary conditions: Consider the problem that entails determining the BOUNDED steady state temperature in a ring centered at 0 with outer radius 6 > 0. The outer ring is maintained at a prescribed temperature of f(e). Determine the eigenfunctions and u(r, 0) in general. That is solve the steady state problem: 1 1 V²u (r, 0) = Urr + ur + 200 = 0, 0 <r<b, 0<0<2″, with BCs r u (r, 0) = u(r, 2π); ue (r, 0) = up (r, 2π); 0<r<b, and u (b, 0) = f(0), 0<< 2π, to obtain the bounded steady state temperature. (b) What is the solution for the special case where f(0) = 1?