International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 555-562
On a class of linear ordinary differential equations having and as solutions
Mathematics Department, University of Jordan, Amman 11942, Jordan
Received 18 March 1994; Revised 25 January 1995
Copyright © 1996 Ahmed D. Alawneh and Ahmed Y. Farah. 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.
We introduced some linear homogeneous ordinary differential equations
which have both formal and finite distributional solutions at the same time, where the finite
solution is a partial sum of the formal one. In the nonhomogeneous case and sometimes in
the homogeneous case we found formal rational and rational solutions for such differential
equations and similarly the rational solution is a partial sum of the formal one.