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Question
Express the following physical statements in the form of differential equation.
The population P of a city increases at a rate proportional to the product of population and to the difference between 5,00,000 and the population
Solution
The rate of change of population increases with respect to time t, is `"d"/"dt"` and the rate of population is proportional to the product of population is `"dP"/"dt"` = kP and the also the difference between 5,00,000 and the population is `"dP"/"dt"` = kP(5,00,000 – P) is required differential equation.
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