Abstract
The aim of this paper is to prove the stability in the sense of Hyers‐Ulam of differential equation of second order y′′ + p(x)y′ + q(x)y + r(x) = 0. That is, if f is an approximate solution of the equation y′′ + p(x)y′ + q(x)y + r(x) = 0, then there exists an exact solution of the equation near to f.
Highlights
Introduction and PreliminariesIn 1940, Ulam 1 posed the following problem concerning the stability of functional equations: give conditions in order for a linear mapping near an approximately linear mapping to exist
In connection with the stability of exponential functions, Alsina and Ger 6 remarked that the differential equation y y has the Hyers-Ulam stability
They dealt with the Hyers-Ulam stability of the differential equation y t λy t, while Alsina and Ger investigated the differential equation y t yt
Summary
The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second order ypxyqxyrx 0. If f is an approximate solution of the equation ypxyqxyrx 0, there exists an exact solution of the equation near to f.
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