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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- Mar 4th 2006, 07:47 PMwankelDiffEq 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 - Mar 4th 2006, 10:12 PMCaptainBlackQuote:

Originally Posted by**wankel**

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

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