Question: 1. (20 points) Solve initial value problem: y + 4y' + 5y = 12(t) y(0) = -1, y'(0) = 1 Hint: (a) (4 pt) Laplace

1. (20 points) Solve initial value problem: y" + 4y' + 5y = 12(t) y(0) = -1, y'(0) = 1 Hint: (a) (4 pt) Laplace transform of both sides. (b) (2 pt) Solve for Ly } (c) (5 pt) Decompose the rational function in Ly}. (d) (9 pt) Do Lapace inverse transform of Lly}, get y. Hint: . (6 pt) Calculate e-2s S( $2 + 45 + 5) . (3 pt) Calculate $ +3 $2 + 4.5 + 5

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