Answer
$y(x)=c_{1}e^{\frac{-2x}{3}}cos(\frac{1}{3}\sqrt{5}x)+c_{2}e^{\frac{-2x}{3}}sin(\frac{1}{3}\sqrt{5}x)$
Work Step by Step
You substitute the $y'', y'$ and $y$ with $y''=r^{2}e^{rx}, y'=re^{rx}$ and $y=e^{rx}$. And by filling out the equation you can find the final equation.
