In we were able to solve an initial-value problem without knowing the Laplace transform
Chapter 4, Problem 62(choose chapter or problem)
In we were able to solve an initial-value problem without knowing the Laplace transform s;{ e -1 . In this problem you are asked to find the actual transformed function Y(s) = s;{ e-1 by solving another initial-value problem. (a) If y = e-i', then show that y is a solution of the initialvalue problem dy dt + 2ty = 0, y(O) = 1. (b) Find Y(s) = s;{e-i'} by using the Laplace transform to solve the problem in part (a). [Hint: First find Y(O) by rereading page 55. Then in the solution of the resulting linear first-order DE in Y(s) integrate on the interval [O, s]. It also helps to use a dummy variable of integration.]
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