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Math Help - Need help separating ODE

  1. #1
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    Need help separating ODE

    How would I separate this equation? I have the solution but I don't know how they arrived there:

    dy/dt = ry(1-(y/K))

    separated form:

    dy/dt = (r/K) * y(K-y)

    Thank you
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  2. #2
    MHF Contributor

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    Re: Need help separating ODE

    Quote Originally Posted by colerelm1 View Post
    How would I separate this equation? I have the solution but I don't know how they arrived there:

    dy/dt = ry(1-(y/K))

    separated form:

    dy/dt = (r/K) * y(K-y)

    Thank you
    That's not a "separated form" at all! If you want to "separate" dy/dt= ry(1- y/K) you can do it simply by dividing both sides by y(1- y/K).

    But what they have done here is the simple algebra "get common denominators and subtract fractions":
    1- \frac{y}{K}= \frac{K}{K}- \frac{y}{K}= \frac{K- y}{K}.
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  3. #3
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    Re: Need help separating ODE

    multiply through ry, factor out r/K leaving, r/K(ky - y^2), which equals r/K(y(K - y))
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