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Rational Solutions of Riccati Differential Equation with Coefficients Rational
並列摘要
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 (Eլ) : y” = ry, r ∈ C(x) is reducible, we look for the rational solutions of Riccati differential equation θ' + θ(superscript 2) = 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.
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