Generalized Hyers-Ulam stability of the second-order linear differential equations (Q410838)

Summary: We prove generalized Hyers-Ulam stability for the second-order linear differential equation \[ y'' + p(x)y' + q(x)y = f(x) \] under the condition that there exists a nonzero \(y_1 : I \rightarrow X\) in \(C^2(I)\) such that \(y_1'' + p(x)y_1' + q(x)y_1 = 0\) and \(I\) is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability for several important well-known differential equations.