Differential Equations

The population of a country changes at a rate proportional to the current size of the population and the prevailing economic situation.  If the economy has a ten year cycle resulting in periods of immigration or emigration

    \[\frac{dN}{dt}=kN+c\sin{\left(\frac{\pi t}{5}+a\right)}\]

where N is the size of the population at time t, measured in years, and k, a and c are constants.  Find an expression for the size of the population at any time.

Source: R.L. Rosenberg. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 45: Question 2, 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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