Pronunciation: (hō"mu-jē'nē-us, -jēn'yus, hom"u-),[key] —adj. 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.
3. Math. 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: x2y3is a homogeneous expression of degree 5. d. relating to a differential equation in which a linear combination of derivatives is set equal to zero.