ODEs: Compute the Laplace transform of f(t) = sin(2t). This requires finding an antiderivative of e^ax sin(bx); we note a quick solution based on a partial formula. We verify our answer using the IVP y"+4y=0, y'(0) = 2, y(0)=0. Finally we note the general formulas for sin(at) and cos(at).
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