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Abstract
We explore the Hyers–Ulam stability of perturbations for a homogeneous linear differential system with \(2\times 2\) constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers–Ulam stable are proven, and for the first time, the best (minimal) Hyers–Ulam constant for systems is found in some cases. Several examples are provided. Obtaining the best Hyers–Ulam constant for second-order constant coefficient differential equations illustrates the applicability of the strong results.
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