Certain properties of the ``universal solution'' (Q1921679)

The author deals with an explicit formula for solutions (the so-called universal solution) of the nonhomogeneous first order differential system \((*)\) \(x'(t)=Ax(t)+f(t)\), where \(A\in \mathbb{R}^{n\times n}\), \(f:\mathbb{R}^n\to \mathbb{R}\), and investigates some properties of this universal solution. The concept of universal solution of \((*)\) was introduced by the author in his paper published in [Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 11(354), 6-13 (1991; Zbl 0786.34002)].