P $9\mathrm{.}4-5$ The circuit shown in Figure P $9\mathrm{.}4-5$ is used in airplanes to detect smokers, who surreptitiously light up before they can take a single puff. The sensor activates the switch, and the change in the voltage $v(t)$ activates a light at the flight attendant's station. Determine the natural response $v(t).$

Answer: $v(t)=-2\mathrm{.}23e^{-2\mathrm{.}1t}+2\mathrm{.}23e^{-37\mathrm{.}9t}V$

Figure P $9\mathrm{.}4-5$ Smoke detector.