Ordinary differential equations Definition

Order of a differential equation

Builds on Ordinary differential equation

Definition

Let $F\left(x, y, y', \dots, y^{(n)}\right) = 0$ be an ordinary differential equation for an unknown function $y$ of $x$ . Its order is the largest integer $k$ such that the equation depends on the derivative $y^{(k)}$ . For a system of equations, the order is the largest order of a derivative that occurs in the system.

Remarks

The equation $y' = x y$ has order $1$ , and the equation $y'' + \sin y = 0$ has order $2$ . The order does not depend on the powers of the derivatives: $(y')^3 = y$ has order $1$ . An equation of order $n$ can be changed into a first-order system of $n$ equations. See reduction to a first-order system.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Differential equation concept
Function concept
Ordinary differential equation definition
Order of a differential equation definition

Where this leads

57 pages build on this one.

Tag	`09M2RDB61G`
URI	`m2://09M2RDB61G`
Kind	definition
Writing	W0 stub
MSC	34A99
Defines	Order of a differential equation
Uses	Ordinary differential equation

Order of a differential equation

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W1

What links here

Used by