Chapter 10.3, Problem 13P

To determine

The solution of the initial value problem $y^{″}+{\omega }^{2}y=\sin \left(nt\right)$, with the initial conditions $y\left(0\right)=0,y^{\prime }\left(0\right)=0$ for ${\omega }^2\ne n^2$ and ${\omega }^2=n^2$.