Question

Please help both questions, thanks

(1 point) Let g(t) = e2 a Solve the initial value problem 4 – 2 = g(t), using the technique of integrating factors. (Do not use Laplace transforms.) y(0) = 0, (t) = b. Use Laplace transforms to determine the transfer function (t) given the initial value problem 6' - 24 = 8(t), (0) = 0. $(t) = c. Evaluate the convolution integral (6 + 9)(t) = Sølt – w)g(w) dw, and compare the resulting function with the solution obtained in part (a). (**g)(t) = dw = (1 point) Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 47+ y = 268(t – 2), y(0) = 0, y'(0) = 0. a. Find the Laplace transform of the solution Y(s) = {y(t)} = b. Obtain the solution y(t) g(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 2. if 0 <t<2, g(t) = if 2 <t<o.