\begin{definition}[Definition:Complementary Function of Linear First Order ODE With Constant Coefficients]
Consider the linear first order ODE with constant coefficients:
:$(1): \quad \dfrac {\d y} {\d x} + a y = \map Q x$
The general solution to the reduced equation:
:$\dfrac {\d y} {\d x} + a y = 0$
is the '''complementary function''' of $(1)$.
From First Order ODE: $\dfrac {\d y} {\d x} = k y$, the '''complementary function''' of $(1)$ is $C e^{-a x}$.
\end{definition}