Differential Equations

A modification to the logistic equation which accounts for the influence of the resources available on the growth of the population results in the equation:

    \[\frac{dN}{dt}=c\frac{\left(K-N\right)N}{K+bN}\]

where b, c and K are positive constants.  Determine the solution of this equation, given that N=N_0 when t=0.  Show that the population size N tends to the carrying capacity of the environment K as t increases.

Source: R.L. Rosenberg. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 45: Question 4, p. 134)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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