# Definition:Differential Equation/Degree/First

< Definition:Differential Equation | Degree(Redirected from Definition:Quasilinear Differential Equation)

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## Definition

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

## Examples

### First Order Quasilinear Ordinary Differential Equation

A first order quasilinear ordinary differential equation is a differential equation which can be written in the form:

- $\map M {x, y} + \map N {x, y} \dfrac {\d y} {\d x} = 0$

### First Order Quasilinear ODE: $x + y y' = 0$

The first order quasilinear ordinary differential equation over the real numbers $\R$:

- $x + y y' = 0$

has the general solution:

- $x^2 + y^2 = C$

where:

- $C > 0$
- $y \ne 0$
- $x < \size {\sqrt C}$

with the singular point:

- $x = y = 0$

## Also see

- Results about
**quasilinear 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