Chapter 5.2, Problem 24P

In each of Problems $23$ through $27$, find the Laplace transformation $Y\left(s\right)=L\left\{y\right\}$ of the solution of the given initial value problem. A method of determining the inverse transform is developed in Section $5.5$.

$y\text{'}\text{'}+y=\{\begin{array}{l}t,0\le t<1,\\ 0,1\le t<\infty ;\end{array}$

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