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 to be stable are proven, first time, best (minimal) systems is found in some cases. Several examples provided. Obtaining second-order equations illustrates applicability strong results.

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...