Bernoulli equation
The Bernoulli equation has the form
dydx+f(x)y=g(x)yk | (1) |
where f and g are continuous real functions and k is a (≠0, ≠1). Such a nonlinear equation (http://planetmath.org/DifferentialEquation) 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:= | (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).
References
- 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 |