\begin{definition}[Definition:Homogeneous Linear Second Order ODE with Constant Coefficients]
A '''homogeneous linear second order ODE with constant coefficients''' is a second order ODE which can be manipulated into the form:
:$y'' + p y' + q y = 0$
where $p$ and $q$ are real constants.
Thus it is a homogeneous linear second order ODE:
:$y'' + \map P x y' + \map Q x y = 0$
where $\map P x$ and $\map Q x$ are constant functions.
\end{definition}