After extensive hard work, this is what I came up with. Assuming that it is correct so far, where do I go from here?
I have a vague understanding that I am supposed to find a relationship of a constant C_n (for each n) with a constant C_0 in getting power series solutions to differential equations but I'm not too sure on how to do anything exactly.
Any help would be greatly appreciated!
Thanks in advance!
If we suppose that the solution of the DE...
... is analytic in x=0, then it can be written as...
(2)
... so that the problem is the computation of the derivatives of y in x=0. The initial conditions give us...
The value of is obtained from (1)...
(3)
... and that means that...
Now You can proceed obtaining by deriving (3), then compute it for x=0 and the setting . An so one...
Kind regards