We explore the Hyers–Ulam stability of perturbations for a
homogeneous linear differential system with 2 × 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.
