A Linear Prelle-Singer method
Abstract
The Prelle-Singer method allows determining an elementary first integral admitted by a polynomial vector field in the plane. It is a semi-algorithm whose nonlinear step consists of determining the Darboux polynomials of the vector field. In this article we construct a linear procedure to determine the Darboux polynomials present in the integrating factor of a polynomial vector field in the plane. Next, we extend the procedure to deal with rational 2ODEs that admit an elementary first integral
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