Polynomial first-order differential equations over matrix skew series

In this paper we establish that a solution to matrix ordinary first-order differential equations with polynomial right side can be reduced to integration of analogous scalar equations if its parameters are triangle. We give conditions upon elements of the sought-for matrix in the case when its parameters are given in the form of dual-diagonal matrices. We consider the Riccati equation over a set of square matrices of the third order. The results are expressed in terms of skew series introduced by the author earlier.