Answer
$y=c_{1}+c_{2}e^{\frac{x}{2}}$
Work Step by Step
$y'=2y''$
$2y''-y'=0$
Use the auxiliary equation
$2r^{2}-r=0$
$r(2r-1)=0$
$r=0$
$2r-1=0$
$r=\frac{1}{2}$
$r_{1}=0$
$r_{2}=\frac{1}{2}$
Formula 8,
$y=c_{1}e^{r_{1}x}+c_{2}e^{r_{2}x}$
$y=c_{1}e^{0}+c_{2}e^{\frac{x}{2}}$
$y=c_{1}+c_{2}e^{\frac{x}{2}}$
