# PP 10.1 - Modeling with Differential Equations Differential...

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Modeling with Differential Equations

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Differential Equations Definition: a differential equation is an equation that contains an unknown function and some of its derivatives. y dt dy 3 = Examples: ) sin( 3 5 2 2 x y dx dy dx y d = - +
Mathematical Modeling Given a real-world problem, mathematical modeling consists of formulating a mathematical description of the problem either from intuitive reasoning or from physical laws. Many mathematical models take the form of differential equations. Solving the differential equation is equivalent to solving the real-world problem.

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Example The rate of growth of a certain population is proportional to its size. The population grows from 3500 people to 6245 people in 8 years. (a) What was the population at the end of the first year ? (b) How long will it take for the original population to double ?
Getting the Model The rate of growth of a certain population is proportional to its size. Let

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PP 10.1 - Modeling with Differential Equations Differential...

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