摘要

We study the algebraic invariant curves and first integrals for the Riccati polynomial differential systems of the form x' = 1, y' = a(x)y(2) + b(x)y+ c(x), where a(x), b(x) and c(x) are polynomials. We characterize them when c(x) = kappa(b(x) - kappa a(x)) for some kappa is an element of C. We conjecture that algebraic invariant curves and first integrals for these Riccati polynomial differential systems only exist if c(x) = kappa(b(x) - kappa a(x)) for some kappa is an element of C.

  • 出版日期2014-10