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Laplace transform and Hyers-Ulam stability of linear differential equations. (English) Zbl 1286.34077
Summary: 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 $y^{(n)}(t)+\sum_{k=0}^{n-1}\alpha_ky^{(k)}(t)=f(t)$ has Hyers-Ulam stability, where $$\alpha_k$$ is a scalar, $$y$$ and $$f$$ are $$n$$ times continuously differentiable and of exponential order, respectively.

##### MSC:
 34D10 Perturbations of ordinary differential equations 34A30 Linear ordinary differential equations and systems, general 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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