I am currently handling the following nonlinear IVP, which has a forcing term as a function of u, which makes this problem a coupled one.

u''+u=A/((1-u)^2) with conditions, u(0)=u'(0)=0. where, A is a real constant.

I intend to solve this using the variational iteration method and get an approximate analytical relation between A and the frequency of oscillation say w.

Note that "w" is not explicitly present in the differential equation.
However for very small values of A, w tends to 1 as it is evident from the DE that RHS will tend to zero for extremely small values of A.

Also at a particular value of A, w tends to zero.

Any help in this regards would be greatly appreciated.

Thank you very much.