Rational solutions of Riccati differential equation with coefficients rational

Abstract

This paper presents a simple and efficient method for determining the rational solution of Riccati differential equation with coefficients rational. In case the differential Galois group of the differential equation (El):y″=ry, r∈C(x) is reducible, we look for the rational solutions of Riccati differential equation θ′+θ2=r, by reducing the number of check to be made and by accelerating the search for the partial fraction decomposition of the solution reserved for the poles of θ which are false poles of r. This partial fraction decomposition of solution can be used to code r. The examples demonstrate the effectiveness of the method.