Definition:Homogeneous


 * Homogeneous (Analytic Geometry): a line or plane is homogeneous if it contains the origin.


 * Homogeneous function: a function $$f: V \to W$$ between two vector spaces over a field $$F$$ is homogeneous of degree $$n$$ if $$f \left({\alpha \mathbf{v}}\right) = \alpha^n f \left({\mathbf{v}}\right)$$ for all nonzero $$\mathbf{v} \in V$$ and $$\alpha \in F$$.


 * Homogeneous differential equation: a first order ordinary differential equation of the form $$M \left({x, y}\right) + N \left({x, y}\right) \frac {dy} {dx} = 0$$, where both $$M$$ and $$N$$ are homogeneous functions.


 * Homogeneous (Physics): of a body, the same all the way through.

Linguistic Note
The word homogeneous comes from the Greek meaning of the same type.