Definition:Second Order Ordinary Differential Equation

Definition

A second order ordinary differential equation is an ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than $2$.

The general second order ODE can be written as:

$\ds \map F {x, y, \frac {\d y} {\d x}, \frac {\d^2 y} {\d x^2} }$

or, using prime notation:

$\map F {x, y, y^\prime, y^{\prime \prime} }$

Also known as

A second order ordinary differential equation is often seen referred to just as a second order differential equation by sources which are not concerned about partial differential equations.

Some sources hyphenate: second-order differential equation.

The abbreviation ODE is frequently seen, hence second order ODE for second order ordinary differential equation.

Also see

• Results about second order ODEs can be found here.

Historical Note

Much of the theory of second order ODEs was progressed by Leonhard Paul Euler.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): second-order differential equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): second-order differential equation