QUESTION 4 i. Use convolution theorem to show that 1 s(s 4) =(cosh 2t ...

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QUESTION 4 i. Use convolution theorem to show that 1 s(s² – 4) =(cosh 2t – 1). ii. Given that r and y are functions of t such that dr = y+1, x(0) = 0, %3D dy 4r + 2H(t - 1), y(0) = -1. dt Use Laplace transforms to solve the system of differential equations. You may use the result from part (i). QUESTION 4 i. Use convolution theorem to show that 1 s(s² – 4) =(cosh 2t – 1). ii. Given that r and y are functions of t such that dr = y+1, x(0) = 0, %3D dy 4r + 2H(t - 1), y(0) = -1. dt Use Laplace transforms to solve the system of differential equations. You may use the result from part (i).