Some remarks on the Shifner-Erougin-Salakhova-Chebotarev type differential equations (Q2038638)

In this work the author studies the problem of solvability in closed form (in quadratures and elemental functions) of linear systems of ordinary differential equations \[ x'= A(t)x \tag{1} \] The main result (Theorem 12) generalizes the results obtained by Shifner, Erougin, Salakhova and Chebotariov. Moreover, the author indicates some ways how to construct \(A(t)\) for which the system is integrable in closed form. In my opinion the discussed in this work problem is very interesting: it is closely connected with the very actual problems of reducibility and stability of linear systems of ordinary differential equations.