No answer up tell now , plz. try again
This is how I'd start it and I'm taking this right out of Rainville and Bedient on the chapter on power series solutions:
Now convert it to the standard form :
with and . That means and leaving for the indicial equation giving roots of 0 and 1. So I'd next go to the section dealing with difference of roots a positive integer by first substituting into the original differential equation and continuing.
Razem, I had some problems going further with this as I've been away from it for some time but I do know the route if I had to solve it: Open the book to the first page of that chapter on power series, start reading, do all of the examples, do a few problems in each section, let it simmer over several days, maybe I don't know about 5-10 problems in all. Eventually, I'd get to the point where I could then go back to this problem and work it. That's really in my opinion how to successfully approach a problem you can't solve in math and elsewhere: put it on the back-burner and work some simpler ones first and then "scale-up" .