Power series to solve 2nd order ordinary differential equations

[hbomb]

I need some help with power series.
I can't remember how to find a power series center around a point.
example question:
y"-xy'-y=0, x=1
I don't how to start this.

 

[radou]

I need some help with power series.
I can't remember how to find a power series center around a point.
example question:
y"-xy'-y=0, x=1
I don't how to start this.

You should find this link useful: http://tutorial.math.lamar.edu/AllBrowsers/3401/SeriesSolutions.asp" .

 

[hbomb]

Yes, thanks. The site has been helpful, but I have a question that I couldn't find an answer for. What happens if you have a summation with the starting index of the summation with n=0 but one of the summations you have an index of n=1. All the exponents are the same.

Also what happens if instead x=1?

 

[courtrigrad]

If you start at n =1, you subtract 1 from the exponent. So:

$$\sum_{n=0}^{k} x^{n} = \sum_{n=1}^{k}x^{n-1}$$