(Problem about a power series solution to a differential equation)

http://f.imgtmp.com/GUbuv.jpg

I feel like I should be getting it right but I am not. Here is what I tried:
http://f.imgtmp.com/Rquv8.jpg

Any help would be greatly appreciated!
Thanks in advance!

Question

(Problem about a power series solution to a differential equation)

http://f.imgtmp.com/GUbuv.jpg

I feel like I should be getting it right but I am not. Here is what I tried:
http://f.imgtmp.com/Rquv8.jpg

Any help would be greatly appreciated!
Thanks in advance!

amistre64 · Answer

at least its homogenous

experimentx · Answer

best of luck http://mathworld.wolfram.com/LegendreDifferentialEquation.html

amistre64 · Answer

$$(x^2+1)y''-xy'+y=0$$
do we do a couchy?

s3a · Answer

I don't think I've encountered a non-homogeneous one.

s3a · Answer

The cauchy statement doesn't ring a bell with me, sorry.

s3a · Answer

Make sure to have a backup of what you're typing just in case since in like 3 min, the site is reloading.

amistre64 · Answer

the laplace transform is a continuous analog of a power series ... so im wonder ing if that applies here

s3a · Answer

Actually, this time I really feel like I've done it right but something is wrong. The problem is very likely a minor mistake that caused everything else following it to be wrong. http://f.imgtmp.com/atw39.jpg A != 9 which is what I get. I didn't write it in my work but it's a direct implication of the last thing I wrote.

amistre64 · Answer

ugh, i cant make it out at the moment :/

s3a · Answer

What? My handwriting?

amistre64 · Answer

well, that too :)  but the whole process in general is just over my head.

s3a · Answer

Lol to my handwriting. It takes sooo much time for me to write nicely and my hand hurts.

It's okay if you forgot how to do this but, I'll try to jog your memory just in case:

1) Summations need same indices.
2) I need a recurrence relation.
3) Use that recurrence relation to find the future coefficients if given the initial coefficient a_0.

(assuming I'm correct).

amistre64 · Answer

:)  theres not much to jog.  i was trying to decipher the content i found online but cant concentrate enough to figure it out.

s3a · Answer

Oh, alright. Thanks anyways. I have to go to class but if someone else sees what my mistake is please tell me. It would allow me to go to bed early tonight :)

amistre64 · Answer

http://www.wolframalpha.com/input/?i=%28x%5E2%2B1%29y%27%27-xy%27%2By%3D0%2C+y%280%29%3D-9%2C+y%27%280%29%3D8 i clicked show steps and it came up blank; even the wolf handwaves this one ;)