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arXiv · 2502.20688

Solving the Riccati Equation

Everardo Rivera-Oliva
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Abstract

In this study, the Riccati equation is resolved using the generalized recursive integrating factor method. By applying a non-linear transformation to the dependent variable $y(x)$ of the Riccati equation, a second-order linear differential equation is derived for a variable $u(x)$ that is related to $y(x)$ through the aforementioned transformation. The second-order differential equation is then addressed using the aforementioned integrating factors method to derive the general solution for $u(x)$, which is subsequently transformed back to obtain the general solution for $y(x)$, thereby resolving the Riccati equation. The general solution to the Riccati equation is presented, followed by solving a few illustrative application examples.

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Everardo Rivera-Oliva. 2025-02-28. Solving the Riccati Equation. https://arxiv.org/abs/2502.20688

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