Question: Please need an answer asap Use the Laplace transform to solve the following initial value problem: I' = 5x + 2y, y' = -3x +

Please need an answer asap

Use the Laplace transform to solve the following initial value problem: I' = 5x + 2y, y' = -3x + e2t I(0) = 0, y(0) = 0 Let X(s) = [{x(t) }, and Y(s) = Cty(t) } Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s) X(s) = Y(s) = Find the partial fraction decomposition of X(s) and Y (s) and their inverse Laplace transforms to find the solution of the system of DES. I(t) = y(t) Consider the initial value problem y" + 49y =cos(7t), y(0) =7, y'(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y (s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). 0-help (formulas) b. Solve your equation for Y (s). Y(s) = [ly(t)} = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t) y(t ) - 1

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