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.

Question

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.

anonymous · Answer

@oldrin.bataku do you know this method?

anonymous · Answer

Let me see...

primeralph · Answer

@goalie2012  Are you very familiar with summations?

anonymous · Answer

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...

primeralph · Answer

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

anonymous · Answer

$$xy''-y'+2y=0$$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.

anonymous · Answer

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).

anonymous · Answer

@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.

anonymous · Answer

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

primeralph · Answer

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

anonymous · Answer

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...

anonymous · Answer

@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?