Definition:Linear First Order Ordinary Differential Equation/Constant Coefficients

Definition
A linear first order ordinary differential equation with constant coefficients is a linear first order ordinary differential equation which is in (or can be manipulated into) the form:
 * $\dfrac {\d y} {\d x} + a y = \map Q x$

where:
 * $\map Q x$ is a function of $x$
 * $a$ is a constant.

It is:


 * Linear because both $\dfrac {\d y} {\d x}$ and $y$ appear to the first power, and do not occur multiplied together


 * First order because the highest derivative is $\dfrac {\d y} {\d x}$


 * Ordinary because there are no partial derivatives occurring in it.

Also see

 * Solution to Linear First Order ODE with Constant Coefficients: Its general solution is:
 * $\ds y = e^{-a x} \paren {\int e^{a x} \map Q x \rd x + C}$
 * where $C$ is an arbitrary constant.