I'm trying to practice on the numerous steps one has to follow to obtain a power series solution so I tried to solve the simple ODE
whos solutions are very well known to be and .
Happily, I laid down the buliding blocks substituting in and, after reindexing and grouping of terms, got the following recurrence relation:
Okay, I tried to continue by assuming once, that and again but I got no pattern at all, I was expecting something familiar - a taylor series expansion at 0.
Question: (1) When to consider 2 cases, a null and a real and the opposite.
(2) Why didn't I get a pattern?