On splitting of linear nonstationary systems of differential equations

Using the matrix asymptotic method, we solve the problem of the splitting of n-order linear nonstationary systems of differential equations into n first-order independent equations for the case where the eigenvalues m_i( t) 1 0,i = 1,...,n,t ? 0,l ] {\mu_i}\left( \tau \right) \ne 0,i = 1,...,n,\tau \in \left {0,\ell } \right] , of the matrix U( t) U\left( \tau \right) determined by the initial system of differential equations are identically equal.