Hello everyone!

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?

Thanks!