Hyers–Ulam stability of linear differential equations of first order, III

Let X be a complex Banach space and let I = (a, b) be an open interval. In this paper, we will prove the generalized Hyers–Ulam stability of the differential equation ty (t)+αy(t)+βtr x0 = 0 for the class of continuously differentiable functions f : I →X, where α, β and r are complex constants and x0 is an element of X. By applying this result, we also prove the Hyers–Ulam stability of the Euler differential equation of second order.  2005 Elsevier Inc. All rights reserved.