An improvement to Darboux integrability theorem for systems having a center Original Research Article

We consider planar polynomial differential systems of degree m with a center at the origin and with an arbitrary linear part. We show that if the system has View the MathML source algebraic solutions or exponential factors then it has a Darboux integrating factor. This result is an improvement of the classical Darboux integrability theorem and other recent results about integrability.