# Category:Formation of Ordinary Differential Equations by Elimination

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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 $k \in \set {1, 2, \ldots, n}$.

## Pages in category "Formation of Ordinary Differential Equations by Elimination"

The following 9 pages are in this category, out of 9 total.

### F

- Formation of Ordinary Differential Equation by Elimination/Examples
- Formation of Ordinary Differential Equation by Elimination/Examples/Parabolas whose Axes are X Axis
- Formation of Ordinary Differential Equation by Elimination/Examples/Simple Harmonic Motion
- Formation of Ordinary Differential Equation by Elimination/Examples/Straight Line through Origin
- Formation of Ordinary Differential Equation by Elimination/Examples/x^2 + y^2 equals a^2
- Formation of Ordinary Differential Equation by Elimination/Examples/y equals A cos 3x + B sin 3x
- Formation of Ordinary Differential Equation by Elimination/Examples/y equals A e^2x + B e^-2x
- Formation of Ordinary Differential Equation by Elimination/Examples/y equals A e^Bx
- Formation of Ordinary Differential Equation by Elimination/Examples/y equals Ax + A^3