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Math Help - 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 P(t)=0, then:

    \frac{dP}{dt}=0,

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

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

    RonL
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