Chapter 3.3, Problem 23P

To determine

To show: The functions, $u\left(t\right)=e^{\lambda t}\cos \mu t\text{ and }v\left(t\right)=e^{\lambda t}\sin \mu t$ are the solutions of the differential equation, $a{y}^{″}+b{y}^{\prime }+cy=0$ which has characteristic equation with complex roots, $\lambda \pm i\mu$.