# Category:Formation of Ordinary Differential Equations by Elimination

This category contains results about Formation of Ordinary Differential Equations 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 with respect to $x$ 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 $k \in \set {1, 2, \ldots, n}$.