Bernoulli Equation

Bernoulli equation

[ber‚nü·lē i′kwā·zhən]

(fluid mechanics)

Bernoulli theorem

(mathematics)

A nonlinear first-order differential equation of the form (dy / dx) + yf (x) = yⁿg (x), where n is a number different from unity and f and g are given functions. Also known as Bernoulli differential equation.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Bernoulli Equation

 

a differential equation of the first order of the form

dy/dx + Py = Qy^α

where P and Q are predetermined continuous functions of x and α is a constant. With the introduction of the new function z = y^-α + ¹, the Bernoulli equation is reduced to a linear differential equation with respect to z. The Bernoulli equation was considered by Jakob Bernoulli in 1695, and a method of solving it was published by Johann Bernoulli in 1697.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.