Chapter 6.3, Problem 31E

In Exercises 27-34

(a) compute the Laplace transform of both sides of the differential equation,
(b) substitute in the initial conditions and simplify to obtain the Laplace transform of the solution, and
(c) find the solution by taking the inverse Laplace transform.

31. $\frac{d^{2}y}{d{t}^2}+4y=\cos 2t,y(0)=-2,y^{\prime }(0)=0$