Find the solution toin terms of power series in the neighbourhood of the origin.

The only real solution that I find is . Do you know if a solution of the formis considered to be in the neighbourdhood of 0 ?

- July 18th 2011, 05:25 AMFractalusquestion about neighboorhood at the origin for a solution to a ODE
**Find the solution to****in terms of power series in the neighbourhood of the origin.**

**The only real solution that I find is . Do you know if a solution of the form****is considered to be in the neighbourdhood of 0 ?** - July 18th 2011, 07:32 AMchisigmaRe: question about neighboorhood at the origin for a solution to a ODE
- July 18th 2011, 07:39 AMFractalusRe: question about neighboorhood at the origin for a solution to a ODE
Thank you for your answer chisigma. I knew this was Euler type but I have to find the solution in terms of in the neighbourhood of 0.

The solution I gave in my last post is correct for . But I don't know if it is considered to be in the neighbourhoud of 0.

Do you understand how I got my solution? You have to use the Euler formula.

Is it helping you?

Regards,

Fractalus - July 18th 2011, 07:55 AMchisigmaRe: question about neighboorhood at the origin for a solution to a ODE
First I must apologize because the errors contained in first stesure of post, errors caused by the 'hurry' for the presence of 'competitors' (Thinking)...

The 'general solution' of ODE is...

(1)

Now function like or are analytic in so that their Taylor series expansion 'somewhere around' exists. But function like or aren't analytic around and that is why doesn't have neither Taylor nor even Laurent expansion around ...

Kind regards

- July 18th 2011, 08:24 AMFernandoRevillaRe: question about neighboorhood at the origin for a solution to a ODE
- July 18th 2011, 08:44 AMFractalusRe: question about neighboorhood at the origin for a solution to a ODE
- July 18th 2011, 09:24 AMchisigmaRe: question about neighboorhood at the origin for a solution to a ODE
An 'old wolf' may lose his teeth and also his memory so that I remember only now a problem I analysed two years ago. The 'general solution' of the ODE...

(1)

... is...

(2)

... where icos(*) and isin(*) are what I called 'I-functions' and their properties I briefly described in ...

http://digilander.libero.it/luposaba...-functions.pdf

In particular the Laurent expansion's coefficients of the I-functions around are computed...

Kind regards

- July 18th 2011, 09:27 AMFractalusRe: question about neighboorhood at the origin for a solution to a ODE
- July 18th 2011, 05:51 PMFractalusRe: question about neighboorhood at the origin for a solution to a ODE
- July 19th 2011, 01:15 AMchisigmaRe: question about neighboorhood at the origin for a solution to a ODE