= Solution
For the normalized equation, $x_0$ is an <ordinary point> when both $p$ and $q$ are analytic near $x_0$. A singular point is a <regular singular point> when $(x-x_0)p(x)$ and $(x-x_0)^2q(x)$ extend analytically to $x_0$; equivalently $p$ has at most a <simple pole> and $q$ at most a double <pole> there.
Thus ordinary points admit ordinary power-series solutions, while the <Frobenius method> applies at a regular singular point. The definitions refer to the coefficients after dividing by the leading coefficient of $y''$.
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