## Question

###### Use the Laplace transform to solve the following initial value problem_y" + 4y = f (t) , y (0) = 2,y' (0) =3wheret < 2 f (t) = {2 t2 2 Procede using the following steps_ Find the Laplace transform of f (t). If Y is the Laplace transform of y; find the Laplace transform of the left side of the differential equation. Solve for Y as a function of $. Find the inverse transform of Y to solve the differential equation Write your final answer as piecewised defined function:

Use the Laplace transform to solve the following initial value problem_ y" + 4y = f (t) , y (0) = 2,y' (0) =3 where t < 2 f (t) = {2 t2 2 Procede using the following steps_ Find the Laplace transform of f (t). If Y is the Laplace transform of y; find the Laplace transform of the left side of the differential equation. Solve for Y as a function of $. Find the inverse transform of Y to solve the differential equation Write your final answer as piecewised defined function:

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