Pronunciation: (hō"mu-jē'nē-us, -jēn'yus, hom"u-), [key]
1. composed of parts or elements that are all of the same kind; not heterogeneous: a homogeneous population.
2. of the same kind or nature; essentially alike.
a. having a common property throughout: a homogeneous solid figure.
b. having all terms of the same degree: a homogeneous equation.
c. relating to a function of several variables that becomes multiplied by some power of a constant when each variable is multiplied by that constant: x2y3 is a homogeneous expression of degree 5.
d. relating to a differential equation in which a linear combination of derivatives is set equal to zero.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.