Chapter 5.2, Problem 19P

In each of Problems $12$ through $21$, transform the given initial value problem into an algebraic equation for $Y=L\left\{y\right\}$ in the $s$- domain. Then find the Laplace transform of the solution of the initial value problem.

$y\text{'}\text{'}+2y\text{'}+5y=t\cos 2t$,

$y\left(0\right)=1,y\text{'}\left(0\right)=0$