Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 793197, 12 pages
doi:10.1155/2010/793197
Research Article

Hyers-Ulam Stability of Differential Equation y′′+2xy′−2ny=0

Soon-Mo Jung

Mathematics Section, College of Science and Technology, Hongik University, Jochiwon 339-701, South Korea

Received 13 October 2009; Accepted 24 November 2009

Academic Editor: Yeol JE Cho

Copyright © 2010 Soon-Mo Jung. 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.

Abstract

We solve the inhomogeneous differential equation of the form y′′+2xy′−2ny=∑m=0∞amxm, where n is a nonnegative integer, and apply this result to the proof of a local Hyers-Ulam stability of the differential equation y′′+2xy′−2ny=0 in a special class of analytic functions.