Question 2 Consider the partial differential equation a²u 22u + Әr2 ду? –25u, 0 < x < 0, 0 < y < . = 7 Use separation of

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Question 2 Consider the partial differential equation a²u 22u + Әr2 ду? –25u, 0 < x < 0, 0 < y < . = 7 Use separation of variables to find all real product solutions u(x, y) = f(x)g(y). Then find a non-zero product solution which satisfies the boundary conditions, Cu(0, 2) = u(T , 3) = 0, 0 < x < 0, = = u(2,0) = u(1, 1) = 0, 0<x<1. xx 0. Finally, show that this boundary value problem is not well posed.