Given the first order initial value problem y' + 2y = 4?(t - 2), y(0) = -2. Let Y(s) denote the Laplace transform of y. Then Y(s) = Taking the inverse Laplace transform we obtain y(t) =
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Step 1: Take the Laplace transform of both sides of the given differential equation: L{y' + 2y} = L{48(t-2)} Using the linearity property of the Laplace transform and the derivative property, we get: sY(s) - y(0) + 2Y(s) = 48(e^-2s / s) Substituting y(0) = -2 Show more…
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