1. ## 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

2. 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