\begin{definition}[Definition:Reduced Equation of Linear ODE with Constant Coefficients/Second Order]
Consider the linear second order ODE with constant coefficients:
:$(1): \quad \dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = \map R x$
The equation:
:$\dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = 0$
is the '''reduced equation''' of $(1)$.
\end{definition}