### Laplace Transform of f(t) = t sin(2t)

ODEs: Find the Laplace Transform of f(t) = t sin(2t). We use the derivative formula for the Laplace Transform: L(y') = sL(y) - y(0) instead of the definition. This method also finds the Laplace transform of g(t) = t cos(2t). We verify the answer by finding the IVP with f(t) as the unique solution.

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