Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 852656, 44 pages
http://dx.doi.org/10.5402/2011/852656
Research Article

Rational Solutions of Riccati Differential Equation with Coefficients Rational

Department of Mathematics, Tunis El Manar University, Tunis 1002, Tunisia

Received 28 March 2011; Accepted 16 April 2011

Academic Editors: H.-T. Hu and X. Meng

Copyright © 2011 Nadhem Echi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Ulmer, β€œOn liouvillian solutions of linear differential equations,” Applicable Algebra in Engineering, Communication and Computing, vol. 2, no. 3, pp. 171–193, 1992. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. J. J. Kovacic, β€œAn algorithm for solving second order linear homogeneous differential equations,” Journal of Symbolic Computation, vol. 2, no. 1, pp. 3–43, 1986. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. M. Bronstein, β€œOn solutions of linear ordinary difference equations in their coeffcient field,” Journal of Symbolic Computation, vol. 29, no. 6, pp. 841–877, 2000. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  4. M. Van Hoeij and J.-A. Weil, β€œAn algorithm for computing invariants of differential Galois groups,” Journal of Pure and Applied Algebra, vol. 117-118, pp. 353–379, 1997. View at Google Scholar
  5. M. Van der Put and F. Ulmer, β€œDifferential equations and finite groups,” Journal of Algebra, vol. 226, no. 2, pp. 920–966, 2000. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  6. I. Kaplansky, An Introduction to Differential Algebra, Hermann, Paris, France, 1957.
  7. M. F. Singer and F. Ulmer, β€œGalois groups of second and third order linear differential equations,” Journal of Symbolic Computation, vol. 16, no. 1, pp. 9–36, 1993. View at Publisher Β· View at Google Scholar Β· View at MathSciNet
  8. M. Van der Put and M. F. Singer, Galois Theory of Linear Differential Equations, Grundlehren der mathematischen Wissenschaften, Springer, Berlin, Germany, 2003.