## Calculus 8th Edition

$y(x)=c_{1}e^{(-1/2+1/2*\sqrt[] 3)x}+c_{2}e^{(-1/2-1/2*\sqrt[] 3)x}$
First write the current derivatives as $y''$ etc. Then 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.