On plugging in $$y = \sum_{n=0}^{\infty}a_nx^{n+s}$$
we have
$$\sum_{n=0}^{\infty}[(n+s)(n+s) - 9]a_nx^{n+s} = 0$$
noting that $a_0 \neq 0$, we find the indical equation gives $s = \pm 3$
on plugging in $s = 3$
$$\sum_{n=0}^{\infty}[n(n+6)]a_nx^{n+3} = 0$$
What are the next steps?. I have to get some sort of relationship on $a_n$. The previous question I have done had $a_n$ and $a_{n-2}$ in it.
Yes, you get $a_n=0$ for $n>0$, thus $$a_0x^3$$ as solution for $s=3$ and $$a_0x^{-3}+a_6x^3$$ for $s=-3$.