Answer
$y=c_{1}e^{\frac{2x}{3}}+c_{2}xe^{\frac{2x}{3}}$
Work Step by Step
$9y''-12y'+4y=0$
Use auxiliary equation,
$9r^{2}-12r+4y=0$
$9r^{2}-12r+4y=0$
$r=\frac{-(-12)±\sqrt ((-12)^{2}-4(9)(4))}{2(9)}$
$r=\frac{12)±\sqrt (144-144)}{18}$
$r=\frac{2}{3}$
Formula 10
$y=c_{1}e^{rx}+c_{2}xe^{rx}$
$y=c_{1}e^{\frac{2x}{3}}+c_{2}xe^{\frac{2x}{3}}$
