Cauchy-Euler

a_{n} x^{n} y^{(n)} + a_{n - 1} x^{n - 1} y^{(n - 1)} + \dots + a_{1} x y^{'} + a_{0} y = g (x), x \in I

Powers of $x$ same order as derivative
2nd order homogenous, try to transform it into form of Constant Coefficient Linear Homogenous ODE
If $I = (0, \infty)$ , use change of variables $x = e^{t}$ ( $\ln x = t$ )
If $I = (- \infty, 0)$ , use $x = - e^{t}$ ( $\ln | x | = t$ )