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Berkovich, L.M. (2000) Transformations of Ordinary Differential Equations: Local and Nonlocal Symmetries. Proceedings of Institute of Mathematics of NAS of Ukraine, 30, 25-34.

has been cited by the following article:

• TITLE: An Analytical Serendipity-Based Technique for Solving the Canonical Riccati Equation

  AUTHORS: Leandro Melendez-Lugo

  KEYWORDS: Differential Equations, Serendipity, Solution Methods, Riccati Equation, Differential Calculus

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.11 No.3, July 11, 2025

  ABSTRACT: Nonlinear differential equations are often extremely difficult to solve. Even three hundred years after its formulation, an analytical solution to the nonlinear Riccati differential equation in its general form remains elusive. Renowned mathematicians such as d’Alembert, Daniel Bernoulli, and Leonhard Euler attempted to solve it without success. In this work, a sui generis technique is introduced to analytically solve the Riccati differential equation in its canonical form, ultimately yielding its general solution.