Need a nudge in the right direction to find the series solution to this differential equation: x*y'' + y' - x*y = 0 centered at x_0 = 2. Where y = Σ c_n * (x- 2) ^ n (where n goes from 0 to ∞). I don't want an answer. What I want to know is how to get the resulting series to be all the same index. More specifically, how do I deal with the "x" terms next to y'' and y?

Question

dumbcow · Answer

you already have y....isn't that the solution ?

anonymous · Answer

I've attached pdf of the problem I am working on. I hope it's legible: http://dl.dropbox.com/u/35467236/Doc-5-8-12%209-56%20PM-page-1.pdf

dumbcow · Answer

its kinda hard to read...but im not great at working with series so i don't think i can help

anonymous · Answer

I kinda get the no one here would be a able to help me with college level math. Oh well, it was worth a try.

anonymous · Answer

(x-2)y'' +2 y'' + y' - (x-2) y + 2 y=0
Write as above.