\begin{definition}[Definition:Formation of Ordinary Differential Equation by Elimination]
Let $\map f {x, y, C_1, C_2, \ldots, C_n} = 0$ be an equation:
:whose dependent variable is $y$
:whose independent variable is $x$
:$C_1, C_2, \ldots, C_n$ are constants which are deemed to be arbitrary.
A '''differential equation''' may be '''formed''' from $f$ by:
:differentiating $n$ times {{WRT|Differentiation}} $x$ to obtain $n$ equations in $x$ and $\dfrac {\d^k y} {\d x^k}$, for $k \in \set {1, 2, \ldots, n}$
:'''eliminating''' $C_k$ from these $n$ equations, for $k \in \set {1, 2, \ldots, n}$.
\end{definition}