Definition:Homogeneous Function/Real Space/Degree

Definition

Let $f: \R^2 \to \R$ be a homogeneous function of two variables:

$\exists n \in \Z: \forall t \in \R: \map f {t x, t y} = t^n \map f {x, y}$

The integer $n$ is known as the degree of $f$.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.7$: Homogeneous Equations