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  "body": "\n## Summary\n\nFor a linear differential equation written with leading coefficient $1$, a point is ordinary when all the coefficients are analytic there, and singular otherwise.\nAt an ordinary point the solutions are themselves analytic, and they can be found as [[power series|08RT9GDDPQ]].\nAt a singular point the solutions may blow up, branch or oscillate wildly.\nThe singular points are split further into [[regular|H96HXG6CA0]] and [[irregular|AT1W4MMTYR]] ones.\nSee the [[definition|T01779NV3Z]].\n\n## Explanations\n\n### L1 human\n\nDivide the equation by the coefficient of the highest derivative.\nWhere the new coefficients are nice power series, nothing special happens: the point is ordinary.\nWhere one of them blows up, the point is singular.\nFor $x y'' + y = 0$, dividing by $x$ gives the coefficient $\\frac{1}{x}$, so $x = 0$ is a singular point and every other point is ordinary.\n",
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