distance over time where acceleration is determinded by distance

Question

So if acceleration is constant then distance is acceleration times time squared. So what if acceleration is determined by distance, say acceleration is equal to the sigmoid function (because that's the first function I thought of, but the solution should work for any function) where x is distance, could you find distance after t time if you knew initial velocity and distance.

Comments

This is not graduate-level, voting to close.

500+ rep users please upvote the closevote linked to if you agree.