Vol. 12, No. 8, 2019

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The variable exponent Bernoulli differential equation

Karen R. Ríos-Soto, Carlos E. Seda-Damiani and Alejandro Vélez-Santiago

Vol. 12 (2019), No. 8, 1279–1291
Abstract

We investigate the realization of a Bernoulli-type first-order differential equation with a variable exponent. Using substitution methods, we show the existence of an implicit solution to the Bernoulli problem. Numerical simulations applied to several examples are also provided.

Keywords
variable exponent differential equations, Bernoulli differential equation, implicit solutions, numerical simulations
Mathematical Subject Classification 2010
Primary: 34A34, 34A09, 34B15, 65L06
Milestones
Received: 6 June 2018
Revised: 18 June 2019
Accepted: 31 August 2019
Published: 25 October 2019

Communicated by Toka Diagana
Authors
Karen R. Ríos-Soto
Department of Mathematical Sciences
University of Puerto Rico at Mayagüez
Mayagüez
Puerto Rico
Carlos E. Seda-Damiani
Department of Mathematical Sciences
University of Puerto Rico at Mayagüez
Mayagüez
Puerto Rico
Alejandro Vélez-Santiago
Department of Mathematical Sciences
University of Puerto Rico at Mayagüez
Mayagüez
Puerto Rico