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Nonlinear first-order differrential equation

  1. Oct 20, 2011 #1
    1. The problem statement, all variables and given/known data

    m*dv/dt = - mg - kv^2, where m,g and k are constants and v(t) is what I should solve

    2. Relevant equations



    3. The attempt at a solution
    At first I solved homogeneous equation m*dvh/dt = -kvh^2 and got vh = m/(kt - cm). Where c is also constant.
    Then I treid to get one solution for the original inhomogeneous equation by subtituting v = f(t)*vh = f(t)*m/(kt - cm) in the original equation, but by it I only got a more difficult differential equation for f(t). So it didn't work.

    I also tried a few different subtitutions at the beginning with no success.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 20, 2011 #2
    You could separate the variables such as:

    dy/dx = f(y)

    integral (dy/f(y)) = integral(dx)

    Initial condition determines integration constant.
     
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