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Unformatted text preview: t 1 ) . Solution: As for the logistic equation, we can proceed as usual: dp dt = apbp 2 Z dp apbp 2 = Z dt Z 1 /a p dp + Z b/a abp dp = t + C 1 /a ln  p  1 /a ln  abp  = t + C 1 a ln ± ± ± ± p abp ± ± ± ± = t + C only care about p > p abp = aCe at p = ( abp ) aCe at p = a 2 Ce at 1baCe at p ( t ) = a/b 1 + e Ceat Now we can determine the remaining constant e C by means of the initial condition, as clearly the limiting population is a b : 1 2 a b = p ( t 1 ) = a/b 1 + e Ceat 1 solving this gives 2 = 1 + e Ceat 1 and hence we have e C = e at 1 Substituting this back in to the general solution gives p ( t ) = a/b 1 + ea ( tt 1 )...
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This note was uploaded on 02/24/2010 for the course MATH MATA35 taught by Professor Martens during the Spring '08 term at University of Toronto.
 Spring '08
 Martens
 Calculus, Logic

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