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Problem 2: Heat Conduction/Diffusion in a Rectangular Plate Consider heat conduction/diffusion in a rectangular plate with the insulated edges. (a) [8 points] Derive the general formula for the distribution of temperature u(x, y, t) on the plate by solving the two-dimensional heat equation in the rectangle under the Dirichlet-Neumann boundary conditions ut = 2√²u, 0<x<a, 0 <y<b, t> 0 ur (0, y, t) = u(a, y, t) = 0 u(x, 0, t) = u(x, b, t) = 0 (b) [2 points] Find the solution for a square plate with a = b = π, if the initial temperature is given by u(x, y,0) = - cos x sin 2y + 2 cos 2x siny - 3 sin 3y + 5 cos 5x sin 5y