Obtain the general solution of

$$x^{2} \frac{d^{2} y}{d x^{2}}+x \frac{d y}{d x}+y=0$$

by using the indicial equation.

Introduce $z=\log x$ as a new independent variable and find an equivalent second order differential equation with constant coefficients. Determine the general solution of this new equation, and show that it is equivalent to the general solution of $(*)$ found previously.