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

by DMOC
Tags: function, logistics, solution, verify
 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$$^{-kCt}$$) 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$$^{-kCt}$$) P(t) = C(1+d*e$$^{-kCt}$$)$$^{-1}$$ -- [I just moved the bottom part to the top.] P(t) = -(e$$^{-t}$$)$$^{-2}$$*-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.

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