(a) Find the solution u(x, y) of Laplace's equation in the rectangle 0 < x < a, 0 < y < b, that satisfies the following boundary conditions u(0, y) = 0, u(a, y) = f(y), 0 < y < b, u(x, 0) = h(x), u(x, b) = 0, 0 ≤ x ≤ a. Hint: Consider the possibility of adding the solutions of two problems, one with homogeneous boundary conditions except for u(a, y) = f(y), and the other with homogeneous boundary conditions except for u(x, 0) = h(x).