Revista de la
Unión Matemática Argentina
A generalized Bernoulli differential equation
Hector Carmenate, Paul Bosch, Juan E. Nápoles, and José M. Sigarreta

Volume 68, no. 2 (2025), pp. 555–575    

Published online (final version): October 8, 2025

https://doi.org/10.33044/revuma.4560

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Abstract

We study a generalized form of the Bernoulli differential equation, employing a generalized conformable derivative. We first establish a generalized variant of Gronwall's inequality, which is essential for assessing the stability of generalized differential equation systems, and offer insights into the qualitative behavior of the trivial solution of the proposed equation. We then present and prove the main results concerning the solution of the generalized Bernoulli differential equation, complemented by illustrative examples that highlight the advantages of this generalized derivative approach. Furthermore, we introduce a finite difference method as an alternative technique to approximate the solution of the generalized Bernoulli equation and demonstrate its validity through practical examples.

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