An integrating factor approach to the Hyers-Ulam stability of a class of exact differential equations of second order (Q2792685)

The author proves the Hyers-Ulam stability for the second-order differential equation NEWLINE\[NEWLINEP(x)y''(x)+Q(x)y'(x)+R(x)=0,\; x\in I=(a,b),\, a,b\in\mathbb{R},NEWLINE\]NEWLINE where \(P\in C^2(I,\mathbb{R})\), \(Q\in C^1(I,\mathbb{R})\), \(R\in C(I,\mathbb{R})\) with \(P(x)\neq 0\) and \(P''(x)-Q'(x)+R(x)=0\) for all \(x\in I\). As a consequence, the Hyers-Ulam stability for the Cauchy-Euler equation NEWLINE\[NEWLINEAx^2 y''(x)+Bxy'(x)+Cy(x)=0NEWLINE\]NEWLINE is obtained, where \(A,B,C\) are real numbers with \(A,C\neq 0\) and \(B=2A+C\).