An ordinary first-order differential equation
where is a real number other than zero or one. This equation was first studied by J. Bernoulli . The substitution converts the Bernoulli equation to a linear inhomogeneous first-order equation, . If , the solution of the Bernoulli equation is ; if , at some points the solution is no longer single-valued. Equations of the type
are also Bernoulli equations if is considered as the independent variable, while is an unknown function of .
|||J. Bernoulli, Acta Erud. (1695) pp. 59–67; 537–557|
|||E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1971)|
|[a1]||E.L. Ince, "Ordinary differential equations" , Dover, reprint (1956)|
Bernoulli equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bernoulli_equation&oldid=40764