We solve the inhomogeneous differential equation of the form y ′′ +2x y ′ -2ny= ∑m=0∞ a m xm, where n is a nonnegative integer, and apply this result to the proof of a local Hyers-Ulam stability of the differential equation y ′′ +2x y ′ -2ny=0 in a special class of analytic functions. Copyright © 2010 Soon-Mo Jung.
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