Definition:Differential Equation/Degree

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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.


Examples

First Degree Second Order

The differential equation:

$\dfrac {\d^2 y} {\d x^2} = k x$

is an example of an order $2$ ordinary differential equation of degree $1$.


Second Degree Second Order

The differential equation:

$\paren {\dfrac {\d^2 y} {\d x^2} }^2 = k x$

is an example of an order $2$ ordinary differential equation of degree $2$.


Also see

  • Results about the degree of a differential equation can be found here.


Sources