1. Not finding help here? Sign up for a free 30min 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!

Help identifying ODE

  1. Sep 16, 2008 #1

    I need help identifying the differential equation: x'' + k(x')^2 + c = 0 . Can anyone point me in the right direction?

  2. jcsd
  3. Sep 16, 2008 #2


    User Avatar
    Homework Helper

    What do you mean by "identifying"? That differential equation could be a model equation for a lot of things! Did you want a specific name for the form or something?

    In any event, if you set x' = v you get a first order ODE,

    v' + kv^2 + c = 0.

    One system that this equation describes is a falling object subject to wind resistance at high velocities, where c would be the acceleration due to gravity, g. (High velocities because at low speeds air resistance tends to go as v instead of v^2).
    Last edited: Sep 16, 2008
  4. Sep 17, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    Mute's dead on. As far as "identifying" is concerned, it is a second order, non-linear equation. As Mute said, letting v= x' you get the first order, separable, differential equation v= -(kv2+ c) or
    [tex]\frac{dv}{kv^2+ c}= -tdt[/tex]

    That's easily integrable but find x from x'= v may give you an integral that has no simple anti- derivative.
  5. Sep 17, 2008 #4
    Thanks - it is in fact an equation for a falling object. V = x' and performing a change of variable gave me the answer I needed.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Help identifying ODE
  1. Help with ODE (Replies: 5)

  2. Help with ODE (Replies: 3)

  3. ODE Help! (Replies: 3)