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