\begin{definition}[Definition:Linear Second Order Ordinary Differential Equation]
A '''linear second order ordinary differential equation''' is a differential equation which is in (or can be manipulated into) the form:
:$\dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = \map R x$
where, as is indicated by the notation, $\map P x$, $\map Q x$ and $\map R x$ are functions of $x$ alone (or constants).
\end{definition}