there is no closed form, like you say, and the additional complexity is around ergodicity, i.e. solutions that start close to each other might end up very far from each other after a certain point. this is also an issue with computer simulations as the error might accumulate and push solutions away. in practice, given the amount of cosmological computations people do on a daily basis, including those for satellites and rockets, this might not necessarily be that big of an issue, but i don't work with that stuff on a daily basis.