$\displaystyle (x^2+2)y'' + 2xy' = 0$
Verify $\displaystyle x=0$ is an ordinary point. Then find a lower bound for the radius of convergence of power series solutions about $\displaystyle x=0$
If you put it in standard form you get
$\displaystyle y'' +\frac{2x}{x^2+2}y'=0$
Since the limit as $\displaystyle \lim_{x \to 0}\frac{2x}{x^2+2}=0$ is finite it is an ordinary point.
The power series will have radius of convergence of at least the distance to the nearest singularity in the complex plane.
$\displaystyle x^2+2=0 \iff x \pm i\sqrt{2}$
So the radius of convergence of at least $\displaystyle R=\sqrt{2}$