Chapter 5.2, Problem 21P

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.

$y\text{'}\text{'}\text{'}\text{'}-6y=t{e}^{-t}$,

$y\left(0\right)=0,y\text{'}\left(0\right)=0,y\text{'}\text{'}\left(0\right)=0,y\text{'}\text{'}\text{'}\left(0\right)=9$