International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 555-562

On a class of linear ordinary differential equations having k=0xkδ(k)(t) and k=0mxkδ(k)(t) as solutions

Ahmed D. Alawneh and Ahmed Y. Farah

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.