Series solutions for 2nd order linear ODEs

jaejoon89

1. The problem statement, all variables and given/known data

Finding series solutions to 2nd order linear ODEs

2. Relevant equations

http://www.math.duke.edu/~wang/108Au05/sec5.7.pdf
(see #s 6 and 7; I attached the link since it would probably look too messy to write it out)

3. The attempt at a solution

For the particular problem I'm working on, there are two roots to the indicial equation. r1 does not equal r2, and the difference is 1.5 so it is NOT an integer. According to my book, for these types of problems we should use the same equations that I referred to in the link, but the answer key for all these problems does not include the r1 or r2 in the summation (i.e., it looks like they did just the summation of a_n * x^n, 1 to infinity, not a_n * r1 * x^n). Can somebody please explain?