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Mathematics LibreTexts

6: Series Solutions

( \newcommand{\kernel}{\mathrm{null}\,}\)

We consider the homogeneous linear second-order differential equation for y=y(x):  P(x)y+Q(x)y+R(x)y=0,

where P(x), Q(x) and R(x) are polynomials or convergent power series around x=x0, with no common polynomial factors that could be divided out. The value x=x0 is called an ordinary point of (???) if P(x0)0, and is called a singular point if P(x0)=0. Singular points will later be further classified as regular singular points and irregular singular points. Our goal is to find two independent solutions of (???).


This page titled 6: Series Solutions is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov via source content that was edited to the style and standards of the LibreTexts platform.

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