In 1–14, solve the given initial value problem using the method of Laplace transforms.

Solution Step 1In this question we have find solution of the given differential equation with the given initial values of the function , using the method of Laplace transform.Given differential equation is - 4y = 4t - 8e-2t Initial value of y at 0 is y(0)=0 and initial value of at 0 is (0)=5Applying the Laplace transform L on both sides of the differential equation we get ,[ ] - 4[y] = 4[t] - 8[e-2t ] ………………………………….(1)