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Or simply, dx^2/dt^2=-GM/x^2

or even more simply,

x''(t)=-k/x^2 where k is a constant.

Does anyone know how to solve this or if it is even possible? I cannot find any resources online for this problem, but I feel like such a simple differential equation would have been attempted or successfully solved by now...

Or is there an easier way to solve this problem - finding x(t) in the gravitational well.

Thanks for any help!