4: Power series methods

Introductory Differential Equations · LibreTexts

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    • 4.1: Power Series
      Many functions can be written in terms of a power series. If we assume that a solution of a differential equation is written as a power series, then perhaps we can use a method reminiscent of undetermined coefficients. That is, we will try to solve for the coefficients of the expansion . Before we can carry out this process, let us review some results and concepts about power series.
    • 4.2: Series Solutions of Linear Second Order ODEs
      This section defines ordinary and singular points and explains how to find a power series solution around an ordinary point for differential equations.
    • 4.3: Singular Points and the Method of Frobenius
      While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.

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    This page titled 4: Power series methods was last modified on Thu, 03 Apr 2025 01:23:33 GMT and is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Vinh Kha Nguyen, Neelam R. Shukla, and Fatemeh Yarahmadi.