Let g(t) = est. a. Solve the initial value problem y - 8y = g(t), y(0)...

   

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Let g(t) = est. a. Solve the initial value problem y - 8y = g(t), y(0) = 0, using the technique of integrating factors. (Do not use Laplace transforms.) y(t) = b. Use Laplace transforms to determine the transfer function p(t) given the initial value problem p' – 80 = 8(1), Þ(0) = 0. Þ(t) = c. Evaluate the convolution integral (o * g)(t) = J p(t – w) g(w) dw, and compare the resulting function with the solution obtained in part (a). (p * g)(t) = . dw = Let g(t) = est. a. Solve the initial value problem y - 8y = g(t), y(0) = 0, using the technique of integrating factors. (Do not use Laplace transforms.) y(t) = b. Use Laplace transforms to determine the transfer function p(t) given the initial value problem p' – 80 = 8(1), Þ(0) = 0. Þ(t) = c. Evaluate the convolution integral (o * g)(t) = J p(t – w) g(w) dw, and compare the resulting function with the solution obtained in part (a). (p * g)(t) = . dw =