# Math 230 - Chapter 6 Study Guide

- Rewrite a linear combination of power series into a single power series.
- Without solving the differential equation, find a lower bound for the radius of convergence about two ordinary points.
- Given the equation involving constants that results after substituting the power series into a differential equation, find two solutions.
- Determine the singular points and classify them as regular or irregular.
- Find the indicial roots and determine whether or not they differ by an integer.
- Find the solution to the Bessel's equation.
- Find the Legendre's Polynomials using Rodrigues' method.
- Solve the Legendre's equation.
- Find two power series solutions about the ordinary point.
- Find two linearly independent power series solutions using the method of Frobenius.

## Notes

- This is a take home exam.
- After setting up the problems, you should use the computer as much as possible to solve them.
- The makelist command in Maxima will be extremely helpful for questions 3, 7, 9, and 10.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Total |

Pts |
4 |
4 |
6 |
4 |
4 |
9 |
3 |
4 |
6 |
6 |
50 |