Please, help me with this one:

I try it, and got the following:

and i stuck here....

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- January 1st 2011, 09:22 AMsinichkoeigenvalue problem
Please, help me with this one:

I try it, and got the following:

and i stuck here.... - January 1st 2011, 11:08 AMInvisibleMan
I get the following DE:

Plugging back I get:

Though I might have mistaken somewhere. - January 1st 2011, 12:01 PMOpalg
- January 1st 2011, 02:18 PMzzzoak
Sorry, there is a mistake in post #2, line 3, last term.

- January 1st 2011, 04:08 PMJester
Your ODE can be solved using a 4th order Darboux transformation. Do you have a second IC for ? Also is or ?

- January 1st 2011, 05:51 PMsinichko
- January 1st 2011, 07:02 PMsinichko
Thanks, but how to continue?

- January 2nd 2011, 12:01 AMsinichko
- January 2nd 2011, 08:04 AMJester
- January 2nd 2011, 08:44 AMOpalg
The equation has eigenfunctions and , with corresponding eigenvalues and (see my comment #3 above).

- January 2nd 2011, 10:14 AMsinichko

I took it from an article: problem (4.8)

Attachment 20309

Wronskian sounds familiar... - January 2nd 2011, 10:17 AMsinichko
- January 2nd 2011, 11:41 AMOpalg
It seemed obvious to me that there should be solutions of the form , for some values of . The reason is that when you differentiate a power of y, it reduces the power by 1 (and when you differentiate twice, the power goes down by 2). So when you put in the expression , each term will be a multiple of either or .

In fact, if then and . Thus

If that is 0 for all y then (putting the coefficients of and equal to 0), you get , from which or ; and , from which or . - January 3rd 2011, 09:39 AMsinichko
Thank you very much