Rational Solutions of Riccati Differential Equation with Coefficients Rational

الملخص EN

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 checks 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.