Solution
= Solution
For an equation $y''+p(x)y'+q(x)y=0$, infinity is a <regular singular point> only when $p(x)=O(x^{-1})$ and $q(x)=O(x^{-2})$. Here $p=-1$ and $q=-2/x-2/x^2$, so infinity is an <irregular singular point>.
= Solution
For an equation $y''+p(x)y'+q(x)y=0$, infinity is a <regular singular point> only when $p(x)=O(x^{-1})$ and $q(x)=O(x^{-2})$. Here $p=-1$ and $q=-2/x-2/x^2$, so infinity is an <irregular singular point>.