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:
 * $f \left({x, y, \dfrac {\mathrm d x} {\mathrm d y}, \dfrac {\mathrm d^2 x} {\mathrm d y^2}, \ldots, \dfrac {\mathrm d^n x} {\mathrm d y^n}}\right) = 0$

or, using the prime notation:
 * $f \left({x, y, y', y'', \ldots, y^{\left({n}\right)}}\right) = 0$