Second-order linear differential equations associated to a Riccati equation of constant coefficients

TL;DR

This paper explores second-order linear differential equations linked to a specific Riccati equation with constant coefficients, using supersymmetric factorizations and a Dirac-like method to extend previous results.

Contribution

It introduces a novel approach combining supersymmetric factorizations and Dirac-like procedures to generate new associated differential equations with additional parameters.

Findings

Derived multiple second-order linear differential equations from a Riccati equation.

Extended existing methods to include up to two more constant parameters.

Provided a minimal extension of previous techniques with broader applicability.

Abstract

We present several second-order linear differential equations that are associated to a particular Riccati equation with only one constant parameter in its coefficients through the technique of supersymmetric factorizations and through a Dirac-like procedure. The latter approach is a minimal extension of the results obtained with the first technique in the sense that it includes up to two more constant parameters