Bernoulli equation

The Bernoulli equation has the form

dydx+f(x)y=g(x)yk (1)

where f and g are continuousMathworldPlanetmath real functions and k is a (0,  1).  Such a nonlinear equation ( is got e.g. in examining the motion of a by yk.  It yields

y-kdydx+f(x)y-k+1=g(x). (2)

The substitution

z:=y-k+1 (3)

transforms (2) into


which is a linear differential equation of first order.  When one has obtained its general solution and made in this the substitution (3), then one has solved the Bernoulli equation (1).


  • 1 N. Piskunov: Diferentsiaal- ja integraalarvutus kõrgematele tehnilistele õppeasutustele.  – Kirjastus Valgus, Tallinn (1966).
Title Bernoulli equation
Canonical name BernoulliEquation
Date of creation 2013-03-22 15:15:03
Last modified on 2013-03-22 15:15:03
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 11
Author pahio (2872)
Entry type Derivation
Classification msc 34C05
Synonym Bernoulli differential equation
Related topic RiccatiEquation