Hyers‐Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

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 .