Answer
$y(x)=c_{1}e^{(\frac{-2}{3}+\frac{2}{3}\sqrt[] 13)x}+c_{2}e^{(\frac{-2}{3}-\frac{2}{3}\sqrt[] 13)x}$
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.
