Answer
$y(x)=c_1+c_2x^{2}$
Work Step by Step
Given: $x^2y''-xy'=0$
In this case the substitution $y(x) = x^r$ yields the indicial equation
$r(r-1)-r=0$
Factor and solve the equation
$r^2-2r=0$
It follows that two linearly independent solutions to the given differential equation are
$y_1(x)=x^0\\
y_2(x)=x^{2}$
so that the general solution is
$y(x)=c_1+c_2x^{2}$
