# Definition:Differential Equation/Ordinary

## Definition

An ordinary differential equation (abbreviated O.D.E. or ODE) is a differential equation which has exactly one independent variable.

All the derivatives occurring in it are therefore ordinary.

The general ODE of order $n$ is:

$\map f {x, y, \dfrac {\d x} {\d y}, \dfrac {\d^2 x} {\d y^2}, \ldots, \dfrac {\d^n x} {\d y^n} } = 0$

or, using the prime notation:

$\map f {x, y, y', y'', \ldots, y^{\paren n} } = 0$

## Also see

• Results about ordinary differential equations can be found here.