Author(s)

Leandro Melendez-Lugo

Instituto Nacional de Investigaciones Nucleares, Centro Nuclear de México, Departamento de Física, City La Marquesa Ocoyoacac, Estado de México, Mexico.

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.

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

Melendez-Lugo, L. (2025) An Analytical Serendipity-Based Technique for Solving the Canonical Riccati Equation . Journal of High Energy Physics, Gravitation and Cosmology, 11, 869-877. doi: 10.4236/jhepgc.2025.113055.