In this problem you will solve the differential equation
[math]

** (1) **
By analyzing the singular points of the differential equation, we know that a series solution of the form [math]**
at least
**
on the interval

** (2) **
Substituting [math]

[math] | c | [math] | c | [math] | c | [math] | c | [math] | [math] [math] [math] | [math] | c | [math] | c | [math] |

** (3) ** In this step we will use the equation above to solve for
some of the terms in the series and find the recurrence relation.

** (a) ** From the constant term in the series above, we know that

c | [math] | c |

c | [math] | c |

c | [math] | c | for | [math] |

** (4) ** The general solution to
[math]

[math]

Your overall score for this problem is