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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:

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

    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

    micromass

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    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

    arildno

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

    HallsofIvy

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    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.
     
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