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Math Help - logistic growth equation

  1. #1
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    logistic growth equation

    Hi, I came across the following differential equation:


    dx(t)/dt=rx(t)*(1-(x(t)/K))


    I am not to sure how to solve it. If i separate the variables i get:

    dx(t)/[rx(t)*(1-(x(t)/K))]=dt

    I dont know how to integrate this

    THanks for you help
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  2. #2
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    Use partial fractions.
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  3. #3
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    Use "partial fractions".
    \frac{1}{x(1- x)}= \frac{A}{x}+ \frac{B}{1- x}
    for some constants A and B.

    I suggest you leave r on the right side of the equation with dt.
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