×

Generalization of the Bernoulli ODE. (English) Zbl 1396.97022

Summary: In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.

MSC:

97I70 Functional equations (educational aspects)
34A34 Nonlinear ordinary differential equations and systems
34A05 Explicit solutions, first integrals of ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bernoulli J. Explicationes, annotationes et additiones ad ea quin actis superiorum annorum de curva elastica, isochrona paracentrica, & velaria, hinc inde memorata, & partim controversa leguntur; ubi de linea mediarum directionum, aliisque novis. Acta Eruditorum. 1695;14:537-553.
[2] Parker AE. Who solved the Bernoulli differential equation and how did they do it? Coll Math J. 2013;44:89-97. · Zbl 1274.01030
[3] Berger RD. Comparison of the Gompertz and logistic equations to describe plant disease progress. Ecol Epidemiol. 1981;71:716-719.
[4] Clark ME, Gross LJ. Periodic solutions to nonautonomous difference equations. Math Biosci. 1990;102:105-119. · Zbl 0712.39014
[5] Nkashama MN. Dynamics of logistic equations with non-autonomous bounded coefficients. Electron J Differ Equat. 2000;2000:1-8.
[6] Scarpello GM, Palestini A, Ritelli D. Closed form solutions to generalized logistic-type nonautonomous systems. Appl Sci. 2010;12:134-145. · Zbl 1189.33007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.