Solve second order nonlinear differential equation

[Alfredo1511]

how do you solve this equation?

y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to Earth only affected by gravitational force. Thank you!

 

[vanhees71]

Is this a homework problem? If so, you should post it in the homework section. So I'll give only a hint to the solution:

You can find a first integral of the equation of motion, which is nothing than energy conservation, by multiplying with $\dot{y}$ (assuming that your prime means in fact a time derivative). Then you get a first-order equation, which can be solved by separation of variables.