Module for the Frobenius Series Solution of a Differential Equation

Numerical Methods for O. D. E.  using Mathematica. (c) John H. Mathews, 2003

Background.

    Frobenius series can be used to solve differential equations at a regular singular point.  The series we substitute is  

    .  

The parameter must be chosen so that when the series is substituted into the D.E. the coefficient of the smallest power of   is zero.  
This is called the indicial equation.  
The recursive equation for the coefficients is obtained by setting the coefficient of    equal to zero.  
We will attempt to have Mathematica solve these tasks.

Example 1.  Use series to solve the D. E.   

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Example 2.  Use series to solve the D. E.   

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Example 3.  Use series to solve the D. E.   

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