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Thread: DiffEq questions

  1. #1
    wankel
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    DiffEq questions

    Without solving the equation, show that the constant functions P(t)=0 and P(t)=K for all t>0 are solutions for the logistic equation
    (dP/dt)=rP(1-(P/500,000))
    K=500,000
    How do I do this? Im so lost, thanks for any responses.
    -ali
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wankel
    Without solving the equation, show that the constant functions P(t)=0 and P(t)=K for all t>0 are solutions for the logistic equation
    (dP/dt)=rP(1-(P/500,000))
    K=500,000
    How do I do this? Im so lost, thanks for any responses.
    -ali
    If $\displaystyle P(t)=0$, then:

    $\displaystyle \frac{dP}{dt}=0$,

    so the LHS of the ODE is zero, and $\displaystyle P=0$ is a root of the
    RHS and so the RHS is also zero, hence $\displaystyle P(t)=0$ is a solution of
    the ODE.

    As $\displaystyle P=K$ is also a root of the RHS and the derivative of
    $\displaystyle P(t)=K$ is also zero this last is also a solution of the ODE.

    RonL
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