Definition of a differential equation

Definition — Differential equation

A differential equation (ODE) is an equation whose unknown is a function $y(x)$ and in which $y$ appears together with its derivative $y'$ (and perhaps $y''$, $y'''$, etc.).

The order of the equation is that of the highest derivative appearing in it: $y' = ky$ is of the first order, $y'' + \omega^2 y = 0$ is of the second order. Solving a differential equation means finding all the functions that satisfy it.

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Topics: Differential equations
Concepts: Differential equation · Order