## goalie2012 one year ago use the frobenius method to solve xy''-y'+2y=0. find index "r" and recurrence relation. compute the first 5 terms(a0-a4) using the recurrence relation for each solution and index r.

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1. goalie2012

@oldrin.bataku do you know this method?

2. oldrin.bataku

Let me see...

3. primeralph

@goalie2012 Are you very familiar with summations?

4. goalie2012

I know that's how this problem should be solved, and I more or less know them, but I still get messed up on some of them. Like this one...

5. primeralph

Cool, @oldrin.bataku should be able to explain it to you. I skip a lot of steps when explaining stuff like that.

6. oldrin.bataku

$$xy''-y'+2y=0$$Observe we may rewrite this in standard form:$$y''-\frac1xy'+\frac2xy=0$$which has a very apparent singular point at $$x=0$$. With a little further attention we can see it's a regular singular point.

7. oldrin.bataku

The method of Frobenius assumes, then, a solution of the form $$y=\sum\limits_{n=0}^\infty a_nx^{r+n}$$ (note our expansion about the singular point).

8. goalie2012

@oldrin.bataku I've tried what I can think of, but I'm not really sure where to go from here. I'm still getting used to and figuring these things out.

9. goalie2012

@oldrin.bataku @primeralph how do I find/get rid of the r value?

10. primeralph

Find the constant number that shifts the power from n to n+r.

11. goalie2012

I'm trying to work it through with my book, but it's not helping. It says to find an indicial equation. still not really sure what to do...

12. goalie2012

@oldrin.bataku I'm so lost. Tried to so something and got a mess. you explained the others very well, could you explain this one to if you're still here somewhere?