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)+βtrx₀=0 for the class of continuously differentiable functions , 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.