Definition:Normal First Order Ordinary Differential Equation

Definition

A first order ordinary differential equation is normal if it is presented in the form:

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

Also known as

Such a first order ODE can also be referred to as in normal form.

Examples

Example: $y' = -x / y$

Consider the first order ordinary differential equation:

$x + y y' = 0$

This can be expressed in normal form as:

$y' = -x / y$

Also see

• Results about normal differential equations can be found here.

Sources

• 1978: Garrett Birkhoff and Gian-Carlo Rota: Ordinary Differential Equations (3rd ed.) ... (previous) ... (next): Chapter $1$ First-Order Differential Equations: $1$ Introduction