Definition:First Order Ordinary Differential Equation

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:

$F \left({x, y, \dfrac {\mathrm d y} {\mathrm d x}}\right)$

or, using prime notation:

$F \left({x, y, y^{\prime}}\right)$

It is convenient, if possible, to present such an equation in the form:

$\dfrac {\mathrm d y} {\mathrm d x} = f \left({x, y}\right)$

or:

$y^{\prime} = f \left({x, y}\right)$

Sources

• George F. Simmons: Differential Equations (1972): $\S 2$