### Laplace Transform Solution of y"-2y'-3y=e^t, y(0) = 0, y'(0) = 1

ODEs: Using the Laplace Transform, find the solution of the IVP y"-2y'-3y=e^t with y(0) = 0, y'(0) = 1. We compute the Laplace transform of f(t) = e^at and derive the formula L(y') = sL(y) - y(0), which plays a central role in the solution.

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