Chapter 4.5, Problem 36P

Determine the general solution of

$y\text{'}\text{'}+{\lambda }^{2}y={\displaystyle \underset{m=1}{\overset{N}{\sum }}{a}_m}\sin m\pi t$,

Where $\lambda >0$ and $\lambda \ne m\pi$ for $m=1,\dots ,N$.