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.
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