\begin{definition}[Definition:Reduced Equation of Linear ODE with Constant Coefficients]
Consider the linear $n$th order ODE with constant coefficients:
:$(1): \quad \ds \sum_{k \mathop = 0}^n a_k \dfrac {\d^k y} {d x^k} = \map R x$
The equation:
:$\ds \sum_{k \mathop = 0}^n a_k \dfrac {\d^k y} {d x^k} = 0$
is the '''reduced equation''' of $(1)$.
\end{definition}