Solve second order nonlinear differential equation

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

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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.
 

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