Laplace transform and Hyers-Ulam stability of linear differential equations

In this paper, we prove the Hyers-Ulam stability of a linear differential equation of the nth order. More precisely, applying the Laplace transform method, we prove that the differential equation y(n)(t)+∑k=0n−1αky(k)(t)=f(t) has Hyers-Ulam stability, where αk is a scalar, y and f are n times continuously differentiable and of exponential order, respectively.