The inhomogeneous Euler equation and its Hyers-Ulam stability (Q2343691)

The authors study the existence of the general solution of the Euler differential equation \[ x^2 y''(x)+\alpha x y'(x)+\beta y(x)=f(x), \] where \(f:[a,b]\to\mathbb{R}\) is a continuous function on \([a,b]\), \(a,b\in\mathbb{R}\) with \(0<a<b\) and \(\alpha, \beta\in\mathbb{R}\), and they prove the Hyers-Ulam stability of the above equation on a bounded domain when the auxiliary equation \[ m^2+(\alpha-1)m+\beta=0 \] has two real roots (distinct or not).