## goalie2012 Group Title 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. one year ago one year ago

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1. goalie2012 Group Title

@oldrin.bataku do you know this method?

2. oldrin.bataku Group Title

Let me see...

3. primeralph Group Title

@goalie2012 Are you very familiar with summations?

4. goalie2012 Group Title

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 Group Title

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 Group Title

$$xy''-y'+2y=0$$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 Group Title

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 Group Title

@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 Group Title

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

10. primeralph Group Title

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

11. goalie2012 Group Title

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 Group Title

@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?