Category:Definitions/Linear Differential Equations

This category contains definitions related to Linear Differential Equations.
Related results can be found in Category:Linear Differential Equations.

A linear differential equation is a differential equation where all dependent variables and their derivatives appear to the first power.

Neither are products of dependent variables allowed.

Hence a linear differential equation is of the form:

$\map {P_0} x y + \map {P_1} x \dfrac {\d y} {\d x} + \map {P_2} x \dfrac {\d^2 y} {\d x^2} + \cdots + \map {P_n} x \dfrac {\d^n y} {\d x^n} = \map Q x$

where $P_0, P_1, \ldots, P_n, Q$ are functions of $x$.