Solve the following ODEs using Laplace transforms: (a) y(i) + 2(1)-y(t)-2y(t) = 0 given y(0) =...

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Solve the following ODEs using Laplace transforms: (a) y(i) + 2ÿ(1)-y(t)-2y(t) = 0 given y(0) = y(0) = 0 and ÿ(0) = 6 (b) y(t) + 4y(1) + 4y(t) = e' given y(0) = y(0) = 0 (c) ÿ(1) - 2y(t) + y(t) = e2t given y(0) = y(0) = -1 (d) ÿ() +2y(t) + y(t) = 3te given y(0) = 4, y(0) = 2 (e) ÿ(1) + 2y(1) + 2y(t) = 5 sin t given y(0) = y(0) = 0 (f) ÿ(1) + 6y(1) +9y(t) = 1212e-31 given y(0) = y(0) = 0 Solve the following ODEs using Laplace transforms: (a) y(i) + 2ÿ(1)-y(t)-2y(t) = 0 given y(0) = y(0) = 0 and ÿ(0) = 6 (b) y(t) + 4y(1) + 4y(t) = e' given y(0) = y(0) = 0 (c) ÿ(1) - 2y(t) + y(t) = e2t given y(0) = y(0) = -1 (d) ÿ() +2y(t) + y(t) = 3te given y(0) = 4, y(0) = 2 (e) ÿ(1) + 2y(1) + 2y(t) = 5 sin t given y(0) = y(0) = 0 (f) ÿ(1) + 6y(1) +9y(t) = 1212e-31 given y(0) = y(0) = 0

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a To solve the differential equation using Laplace transforms well denote the Laplace transform of yt as Ys Taking the Laplace transform of the given equation and applying the initial conditions we ha... View the full answer