\begin{definition}[Definition:Second Order Ordinary Differential Equation]
A '''second order ordinary differential equation''' is an ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than $2$.
The general '''second order ODE''' can be written as:
:$\ds \map F {x, y, \frac {\d y} {\d x}, \frac {\d^2 y} {\d x^2} }$
or, using prime notation:
:$\map F {x, y, y^\prime, y^{\prime \prime} }$
\end{definition}