1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve second order nonlinear differential equation

  1. Sep 7, 2015 #1
    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!
  2. jcsd
  3. Sep 7, 2015 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook