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!

Seemingly Non-Separable Differential Equation

  1. Nov 1, 2012 #1
    1. The problem statement, all variables and given/known data

    I am trying to find the parametric equation that describes the following second order differential equation:

    2. Relevant equations

    [itex]m\frac{d^2y}{dt^2}=-mg - k\frac{dy}{dt}[/itex]

    Where m, g, and k are all constants.

    3. The attempt at a solution

    I substituted [itex]u=\frac{dy}{dt}[/itex] to reduce the order of the equation to one. Now I have:


    And I have been stuck here. I don't see how to separate the variables, can anybody help out?
  2. jcsd
  3. Nov 1, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    It's just a linear differential equation with constant coefficients. Have you seen how to solve these??
  4. Nov 1, 2012 #3
    I have seen how to solve simple ones. My main problem here is isolating t and u. The algebra doesn't work out, and I've been so far unsuccessful in finding a substitution that will separate these variables.
  5. Nov 1, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Find a suitable CONSTANT addition to "u"
  6. Nov 1, 2012 #5


    User Avatar
    Staff Emeritus
    Science Advisor

    Since there is no variable, t, itself in the equation, it is pretty trivial to separate!

    [itex]m\frac{du}{ku+ mg}= - dt[/itex]

    Now integrate both sides.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Seemingly Non-Separable Differential Equation