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: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