Definition:Differential Equation/Degree

Definition

Let $f$ be a differential equation which can be expressed as a polynomial in all the derivatives involved.

The degree of $f$ is defined as being the power to which the derivative of the highest order is raised.

By default, if not specifically mentioned, the degree of a differential equation is assumed to be $1$.

First Degree (Quasilinear)

A quasilinear differential equation is a differential equation of the first degree.

Sources

• 1926: E.L. Ince: Ordinary Differential Equations ... (previous) ... (next): Chapter $\text I$: Introductory: $\S 1.1$ Definitions
• 1952: H.T.H. Piaggio: An Elementary Treatise on Differential Equations and their Applications (revised ed.) ... (previous) ... (next): Chapter $\text I$: Introduction and Definitions. Elimination. Graphical Representation: $3$. Definitions
• 1956: E.L. Ince: Integration of Ordinary Differential Equations (7th ed.) ... (previous) ... (next): Chapter $\text {I}$: Equations of the First Order and Degree: $1$. Definitions
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): differential equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): differential equation