# Definition:First Order Ordinary Differential Equation

Jump to navigation
Jump to search

## Definition

A **first order ordinary differential equation** is an ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than $1$.

The general **first order ODE** can be written as:

- $\map F {x, y, \dfrac {\ d y} {\ d x} }$

or, using prime notation:

- $\map F {x, y, y'}$

If it is possible to do so, then it is often convenient to present such an equation in the form:

- $\dfrac {\d y} {\d x} = \map f {x, y}$

that is:

- $y' = \map f {x, y}$

## Sources

- 1962: J.C. Burkill:
*The Theory of Ordinary Differential Equations*(2nd ed.) ... (previous) ... (next) - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1.2$: General Remarks on Solutions