Consider the initial value problem y - 4y' + 4y = f(t), y(0) = 2, y'(0)...

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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) 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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