Answer
$y=e^{-x}(c_{1}cos(\frac{x}{10})+c_{2}sin(\frac{x}{10}))$
Work Step by Step
$100\frac{d^{2}P}{dt^{2}}+200\frac{dP}{dt}+101P=0$
$100P''+200P'+101P=0$
Use auxiliary equation,
$100r^{2}+200r+101=0$
$r=\frac{-200±\sqrt((200)^{2}-4(100)(101))}{2(100)}$
$r=\frac{-200±20\sqrt(100-101)}{200}$
$r=\frac{-200±20i}{200}$
$r= -1±\frac{1}{10}i$
$r_{1}=-1+\frac{1}{10}i$
$r_{2}=-1-\frac{1}{10}i$
$α=-1$, $β=\frac{1}{10}$
Formula 11
$y=e^{αx}(c_{1}cosβx+c_{2}sinβx)$
$y=e^{-x}(c_{1}cos(\frac{x}{10})+c_{2}sin(\frac{x}{10}))$
