Solve the following initial-boundary-value problem by using the separation of variables technique: Utt UTI, with the prescribed boundary conditions u(0, t) = 0, u(1, t) = 0, ana une initial conditions where f(x) = a(1-x) 1-a 7 (0 ≤ x ≤1, ,t> 0), ut(x,0) = 0, t>0, 0 < x < 1 u(x,0) = f(x), for 0≤x≤ a, for a ≤x≤ 1, with 0 < a < 1.

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