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Mathematics

Differential Equations and Their Classification by Order and Linearity

Quick fact

The order of a differential equation is the highest derivative it contains, and linearity depends on whether the unknown function and its derivatives appear only to the first power and are not multiplied together—so y'' + y = 0 is linear and second-order, while (y')² + y = 0 is nonlinear and first-order.

Why this is interesting

You’ve probably seen equations like y' = ky that describe how a population grows or how a cup of coffee cools. But how do mathematicians categorize all the different ways derivatives can appear in an equation?

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Differential Equations and Their Classification by Order and Linearity

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