
#1
Sep2109, 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(CP). 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. 


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