Seek a power series solution about of the equation

as far as the term in . Then find a closed-form of the solution (i.e. write the solution using simple functions, in this case arctan, rather than infinite series) by using

.

It's the closed-form bit that's confusing me, 'cause my answer looks nothing like the arctan thing. The answer I got was

where A is just a constant.

(Worried)

Can anyone help?