(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In Problems 25–30, x=0 is a regular singular point of

the given differential equation. Show that the indicial

roots of the singularity differ by an integer. Use the method

of Frobenius to obtain at least one series solution about

x=0.

http://gyazo.com/ef4d819c3a6f0b820f1dfc16e01889d2

3. The attempt at a solution

If someone wants me to I will right out what I did but basically what it came out to is

(r(r-1)+r)c_{0}x^{r-1}+[itex]\sum[/itex](C_{n+1}(n+1+r)(n+r) + C_{n+1}(n+1+r)+C_{n})x^{n+r}

now if you solve for r you get

r^2-r+r and r_{1,2}=0

you put this into this

C_{n+1}(n+1+r)(n+r) + C_{n+1}(n+1+r)+C_{n}=0 and rearrange it a bit to make it simple and you got the setup for a recursion formula

Now if you try using the recursion formula to solve for a y1 you will see that when you let n=0 you will get a 0 on the bottom making it undefined

and I know you can use this

http://gyazo.com/a3e25290c490344eae98c9b7f9e59f3f

if this happens in y2 but what happens when your trying to solve for y1 and this happens?

OR did I mess up somewhere(I dont think I did because I double checked my work)?

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# Homework Help: Using Frobenius theorem

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