Definition:Differential Equation/Ordinary

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An ordinary differential equation is a differential equation which has exactly one independent variable.

All the derivatives occurring in it are therefore ordinary.

The general ordinary differential equation 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 known as

The term ordinary differential equation is often presented in its abbreviated form ODE or O.D.E.

Also see

  • Results about ordinary differential equations can be found here.