I have the encountered a singularity in the equation below . $$ y^{\prime \prime}(x)+\frac{2}{x} y^{\prime}+\left[y-\left(1+\frac{2}{x^2}\right)\right] y(x)=0, \quad 0<x<+\infty, $$ with conditions $$ y \in C[0,+\infty), \quad y(+\infty)=0 $$
I tried to remove the singularity by referring to Bessel functions. I also tried to examine the asymptotic behaiour of the ODE by first eliminating the smallest terms i.e $ \dfrac{2}{x} y^{\prime} $ and $ \dfrac{2}{x^2}$ Before i code the solution numerically. However , the equation seems to be more relatable with Emden - Fowler equations and the Lane- Emden equations as explained here. Is there any way i could be helped to over come this singularity ? Any suggestions are highly welcome.