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Homework Help: First order linear differential equation

  1. May 7, 2013 #1
    1. The problem statement, all variables and given/known data

    dy/dt = k*y*ln(y/M), where M and k are constants.

    Show that y = Meaekt satisfies the above equation for any constant a.

    2. Relevant equations

    y' = ky
    y = P0ekt

    3. The attempt at a solution

    Taking the derivative of y, I get:


    which is,


    ..and I'm stuck here.


    Nevermind, I figured it out.

    ln(y) = ln(M) + ae^(kt)

    ae^(kt) = ln(y/M)

    Plugging back in...


    Last edited: May 7, 2013
  2. jcsd
  3. May 8, 2013 #2


    User Avatar
    Science Advisor
    Homework Helper

    Well done! :)
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