Chapter 4.4, Problem 15P

Show that the solution of the initial value problem $\begin{array}{ccc}my\text{'}\text{'}+\gamma y\text{'}+ky=0,& y\left(t_0\right)=y_0,& y\text{'}\left(t_0\right)=y_1\end{array}$ can be expressed as the sum $y=v+w$ where $v$ satisfies the initial conditions $v\left(t_0\right)=y_0,v\text{'}\left(t_0\right)=0,$ $w$ satisfies the initial conditions $w\left(t_0\right)=0,w\text{'}\left(t_0\right)=y_1$, and both $v$ and $w$ satisfy the same differential equations as $u$. This is another instance of superposing solutions of simpler problems to obtain the solution of a more general problem.