Having the equation $$x^{2}y''+xy'+x^{2}y=0$$
I get the indicial equation at get r=0, and am left with the equation. $$r^{2}a_{0}x^{r}+(r^{2}+2r+1)a_{1}x^{r+1}+\sum^{\infty}_{0}\big[[(n+r+2)(n+r+1)+(n+r+2)]a_{n+2}+a_{n}\big]x^{n+r+2}=0$$
subbing in r=0 gives: $$a_{1}x+\sum^{\infty}_{0} [(n+2)^2a_{n+2}+ a_{n}]x^{n+2}=0$$
So im not sure how to get the recurrence relation as i don't have an $a_{n+1}$ to find this and also i have an $a_{1}$ term so am not sure how to find this. Any help would be appreciated thank you.