Homogeneous Functions
One is that a first-order ordinary differential equation is homogeneous (of degree 0) if it has the form
where x is an independent variable, y a dependent variable, and M(x, y) and N(x, y) are homogeneous functions of degree n; in other words scalar multiplying each variable by a constant λ leaves the function unchanged:
- .
In a more general form:
- .
Read more about this topic: Homogeneous Differential Equation
Famous quotes containing the words homogeneous and/or functions:
“If we Americans are to survive it will have to be because we choose and elect and defend to be first of all Americans; to present to the world one homogeneous and unbroken front, whether of white Americans or black ones or purple or blue or green.... If we in America have reached that point in our desperate culture when we must murder children, no matter for what reason or what color, we don’t deserve to survive, and probably won’t.”
—William Faulkner (1897–1962)
“Empirical science is apt to cloud the sight, and, by the very knowledge of functions and processes, to bereave the student of the manly contemplation of the whole.”
—Ralph Waldo Emerson (1803–1882)