Motion in gravitational field?

I want to find out the true equations of motion of an object released at an initial velocity 'u' in a gravitation field of another object (like the earth). Assume that the frame of reference is such that one of the object is in the origin all the time. I just need some guidance in arriving at the differential equation. I don't want an approximation, so it is not a uniform gravitational field and potential energy is not mgh (which is approximation). Also assume there is no air resistance etc and do not consider effects of general relativity. Thank you. All I need is the initial equation which I am having trouble to come up with.