\begin{definition}[Definition:Homogeneous Linear Second Order ODE]
A '''homogeneous linear second order ODE''' is a differential equation which is in (or can be manipulated into) the form:
:$\dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = 0$
where, as is indicated by the notation, $\map P x$ and $\map Q x$ are functions of $x$ alone (or constants).
\end{definition}