Seek power series solutions of the given differential equation

[hc23881]

I know there are a number of ways to do this problem, to increment the series etc. but, would someone please be able to explain how they get the answers for this problem simply and easily
?

Thanks!

A screen shot is attached

 

[SteamKing]

I know there are a number of ways to do this problem, to increment the series etc. but, would someone please be able to explain how they get the answers for this problem simply and easily
?

Thanks!

A screen shot is attached

I take it you haven't tried to read your own figure. You'll need to post something larger than a < 40kB thumbnail.

 

[RUber]

Alternatively, you could actually type in the problem so we can all read it on the page.