Bernoulli equation

An ordinary first-order differential equation

where is a real number other than zero or one. This equation was first studied by J. Bernoulli [1]. The substitution converts the Bernoulli equation to a linear inhomogeneous first-order equation, [2]. 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 .

References

[1]	J. Bernoulli, Acta Erud. (1695) pp. 59–67; 537–557
[2]	E. Kamke, "Differentialgleichungen: Lösungen und Lösungsmethoden" , 1. Gewöhnliche Differentialgleichungen , Chelsea, reprint (1971)

References

[a1]	E.L. Ince, "Ordinary differential equations" , Dover, reprint (1956)