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.