Hi, I am having trouble solving this problem, please help me figure this one out. Thanks in advance.

xy'' + y' + xy=0 at ordinary point x=1.

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- May 28th 2009, 02:08 AMwarmonk102Series Solutions Near an Ordinary Point help please
Hi, I am having trouble solving this problem, please help me figure this one out. Thanks in advance.

xy'' + y' + xy=0 at ordinary point x=1. - May 29th 2009, 05:16 AMchisigma
With the substitution the equation becomes...

(1)

That is an 'incomplete' linear ODE and we will search an analytic solution written as...

(2)

If we derive from (2) le derivatives of and subsitute them in (1) we arrive to write the following 'infinite sysytem' of algebric equations...

(3)

... whose solution is...

(4)

Since a solution of (1) multiplied by a constant is also a solution of (1), we can set without limitations and so with (4) we derive...

The searched solution od (1) is then...

(5)

Kind regards