Use power series to solve (1+x^2)y''+xy'+(3x+2)y=0

Question

tkhunny · Answer

Well, are you expecting someone else to drag through that for you?  Let's see where you started, at least.

ikram002p · Answer

well maybe he/she dont know the steps :O

ikram002p · Answer

@keynote  start by dividing term on leading coefficient

anonymous · Answer

I got into the substitution and am stuck there

ikram002p · Answer

oh then type what u got so far

tkhunny · Answer

See, this is what I am talking about.  Let's see your work so a wonderful, kind, and giving volunteer doesn't have to do it for you.  Very good.

anonymous · Answer

$$\sum_{n=2}^{\infty} n(n-1)a_nx^{n-2}+\sum_{n=2}^{\infty} n(n-1)a_nx^{n}+\sum_{n=1}^{\infty} na_nx^{n}+\sum_{n=0}^{\infty} 3a_nx^{n+1}+\sum_{n=0}^{\infty} 2a_nx^{n}+$$

anonymous · Answer

That's what i have so far

tkhunny · Answer

That's excellent.  Now, you just have to change your indeces so they match up.  You can't have one start at 0, one at 1 and the other at 2.

Mind you, I can't really tell if that is right, since it is cut off by the screen.  It does appear to me that you have the right idea.

anonymous · Answer

So how do i change the indeces. Thats where my problem is

tkhunny · Answer

Very carefully...

$\sum\limits_{n=1}^{\infty}na_{n}x^{n} = \sum\limits_{n=0}^{\infty}(n+1)a_{n+1}x^{n+1}$

That's about it.