HYERS-ULAM STABILITY OF LINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER WITH CONSTANT COEFFICIENT

Abstract

Y. Li and Y. Shen [12] have proved the Hyers-Ulam stability of differential equation y′′(x) + αy′(x) + βy(x) = 0, in the condition that its characteristic equation has two different positive roots.  In this paper, we prove that the differential equation y′′(x) + αy′(x) + βy(x) = 0 has the Hyers-Ulam stability, no matter whether its characteristic roots are real or complex.  Therefore the results obtained in this paper improve and extend the ones of [12].