What is an ordinary differential equation equation that is yet to be solved? In another word, the ODE i am talking about is very special that an special method must be developed in order to solve solely that ODE approximately in infinite series.
An standard method mean it could solve an class of general ODEs.
I am wondering are there any, You could just give one example and its reference if you want.
"Yet to be solved" literally mean mathematician can't figure out its solution(I don't meant that the equation that have no solution at all)
 A: There are many, if you're allowing initial value problems. Any differential equation that has a solution of a definite integral that doesn't have a closed form antiderivitive is potentially an open problem, since the problem of an algorithm for determining the existence of closed form definite integrals is a great open problem related to transcendence theory. 
The Risch integration algorithm is the answer to the question of the existence of a closed form antiderivitive, so we can tell (somewhat, it's a semi-algorithm somewhat analogous to testing a first order statement for validity) if any differential equation that has an indefinite integral for the solution. We have no similar algorithm for the closed form definite integral where we lack a closed form antiderivitive. We have some heuristics for some definite integrals, and others we simply don't know if they exist.
An example is a differential equation for an initial value problem that has the Euler-Mascheroni Constant as a solution to an initial value problem. 
http://mathworld.wolfram.com/Euler-MascheroniConstant.html
