Geodesic
Polynomial first-order differential equations over matrix skew series
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2014), pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: matrix differential equations, decreasing of the order, skew series. 
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     author = {V. P. Derevenskii},
     title = {Polynomial first-order differential equations over matrix skew series},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--16},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_9_a0/}
}
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V. P. Derevenskii. Polynomial first-order differential equations over matrix skew series. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2014), pp. 3-16. http://geodesic.mathdoc.fr/item/IVM_2014_9_a0/

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