(a) Find the Laplace transform of the function -{ f(1) = e', 0 ...

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(a) Find the Laplace transform of the function -{₁ f(1) = e', 0 <1 <1, 1, > 1. (b) Use the Laplace transform to solve the given initial - value problem. y"-6y +9y = 0, subject to y(0) = 1, y'(0) = 4. (c) Find the following inverse Lapalce transform [!] (d) Use the Convolution theorem to evaluate the given inverse Laplace transform 2-₁ [ ]· ss (s-1)² (a) Find the Laplace transform of the function -{₁ f(1) = e', 0 <1 <1, 1, > 1. (b) Use the Laplace transform to solve the given initial - value problem. y"-6y +9y = 0, subject to y(0) = 1, y'(0) = 4. (c) Find the following inverse Lapalce transform [!] (d) Use the Convolution theorem to evaluate the given inverse Laplace transform 2-₁ [ ]· ss (s-1)²