Register to reply

I need to verify that a function is a solution of a logistics DE

Tags: function, logistics, solution, verify
Share this thread:
Sep21-09, 08:50 AM
P: 100
1. The problem statement, all variables and given/known data

Verify by direct cauculation that if k, C, and d are constants, then the function P(t) = C/(1+d*e[tex]^{-kCt}[/tex]) is a solution of the logistic DE P' = kP(C-P).

2. Relevant equations

I don't think there are any for this problem. :)

3. The attempt at a solution

Okay, so ... uh ... I guess in this problem I should just be looking for the derivative of the original equation. So here goes ....

P(t) = C/(1+d*e[tex]^{-kCt}[/tex])
P(t) = C(1+d*e[tex]^{-kCt}[/tex])[tex]^{-1}[/tex] -- [I just moved the bottom part to the top.]
P(t) = -(e[tex]^{-t}[/tex])[tex]^{-2}[/tex]*-1 (chain rule) <-- I think this is where I go wrong. C, k, and d are constants so I just made their derivaties one. Is that the right thing to do? Because somehow I get the feeling that the third line of work here isn't going to get me to the answer.
Phys.Org News Partner Science news on
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history

Register to reply

Related Discussions
Can someone verify my solution? Differential Equations 3
Partial derivatives - verify solution? Calculus & Beyond Homework 2
Help me to verify the piecewise function answers Calculus & Beyond Homework 1
Appropriate predator-equilibrium Differential Equations 1