\begin{definition}[Definition:Linear Second Order ODE with Constant Coefficients]
A '''linear second order ODE with constant coefficients''' is a second order ODE which can be manipulated into the form:
:$y'' + p y' + q y = \map R x$
where:
:$p$ and $q$ are real constants
:$\map R x$ is a function of $x$.
Thus it is a linear second order ODE:
:$y'' + \map P x y' + \map Q x y = \map R x$
where $\map P x$ and $\map Q x$ are constant functions.
\end{definition}