Question: Consider the initial value problem y - 4y' + 4y = f(t), y(0) = 2, y'(0) = 5. The function f(t) is defined as

Consider the initial value problem y" - 4y' + 4y = f(t),

Consider the initial value problem y" - 4y' + 4y = f(t), y(0) = 2, y'(0) = 5. The function f(t) is defined as (b) f(t)= e2t-2 cos(3t - 3) u(t-1) where u(t) is the Heaviside function. (a) Find the Laplace Transform of f. (10 marks) Hence, determine the solution of the initial value problem using Laplace Transform. (20 marks)

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