36 Let C be the circle r = a in the xy plane and the region interior to C. Derive the solution of the boundary-value problem Au = x - y in R u=0 on C in the form (4-ar) cos 20 u(r,0) 12 Hint: Examine the form of the function on the right in the differential equation, and derive the particular solution rcos 20 12 12 of the Poisson equation. Now derive the solution of the Dirichlet problem w = 0 in R w(a,0) = v(a,0) on C