The distance from the Earth at a given time t for a body moving toward the Earth.

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Suppose an object is moving toward the Earth(with a direction perpendicular to the Earth's surface) at an initial speed v0, starting from a distance r0. The object also experiences gravitational acceleration. Is it possible to obtain an expression of r as a function of t? In other words, whats the distance from the Earth at a time t?

I tried solving this second order differential equation:
d2r/dt2 = GM/r2

I ended up with a mess of stuff. And it seems impossible to make r the subject of the equation.
 

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