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Solve the following problems (a) Find the eigenvalues and eigen-functions for the problem f" (x) + Af(x) = 0, f(0) =0, f'(2) =0 (b) Discuss the orthogonality relation for the eigen-functions in part (a) (c) Find the general solution of the problem u(x, t) =guzz(x, t), 05x52, t>0 u(0, t) =0, ux(2, t) = 0