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I am swiftly learning that past the undergraduate level we can't really solve anything explicitly, unless we are really lucky with the problem. In my research I have an ODE which is nonlinear and nonautonomous and is awkward to analyse.

My question is this: given some information about the solution to the ODE, is it possible to deduce an approximate formula for the solution or some more information about it? In my particular case, from simulation I expect the solution to be a periodic function in the asymptotic limit; can I use this to say much more?

Cheers,

Tom