Are you SURE you've written it correctly?
As it is written, I'm tempted to subtract 1 and set up a very simple system where f = y' and f' = y".
We suppose that the solution of the second order linear DE...
, , (1)
... can be expressed as McLaurin series, so that is...
(2)
Now it is possible to find how many terms of the (2) You like, starting from the first two that are given as 'initial conditions'. From (1) we derive as ...
(3)
From (3) we derive as...
(4)
From (4) we derive as...
(5)
At this point it is evident that is so that the solution of (1) is [simply] ...
Kind regards