Answer
$y=c_{1}e^{2x}+c_{2}e^{6x}$
Work Step by Step
$y''-8y+12y=0$
Use auxiliary equation
$r^{2}-8r+12=0$
$r^{2}-8r+12=0$
$(r-2)(r-6)=0$
$r=2,r=6$
By Theorem 4,
$y=c_{1}e^{r_{1}x}+c_{2}e^{r_{2}x}$
$y=c_{1}e^{2x}+c_{2}e^{6x}$
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