Consider the equation $x^2y''+2xy'-(6+x)y=0$. $x=0$ is a regular singular point.

One can try solutions of the form $y=x^r\sum_{n=0}^{\infty}a_nx^n$, $a_0\neq 0$.

The equation that $r$ satisfies is called the indicial equation.

The roots of the indicial equation are the exponents.

Find the possible exponents at this regular singular point.