Use Laplace transform to solve the following initial value problems 1 2 y 10y 9y 5t y 0 1 g 0 2 y 3y 2y e y 0 1 y 0 0 3 y 6y 15y

Question

Use Laplace transform to solve the following initial value problems 1 2 y 10y 9y 5t y 0 1 g 0 2 y 3y 2y e y 0 1 y 0 0 3 y 6y 15y 2 sin 3t y 0 1 y 0 4 Question 2 Find the Fourier series representation of the following function f x 0 x 0 x 0 x and has period 2 Question 3 Find the Fourier transform of the following function f x x x 1 otherwisu

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