Geodesic
Integrable Systems of Linear Ordinary Differential Equations of General Order
Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 52-65.

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In this paper, we define sufficient conditions for the solvability in quadratures of systems of linear ordinary differential equations of higher orders with variable coefficients. The method of variation of constants for equations of higher orders and for systems of equations of first order is generalized to the case of such systems. Results are obtained by reducing the systems under consideration to matrix equations of higher orders studied by methods of the theory of Lie algebras. 
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V. P. Derevenskii. Integrable Systems of Linear Ordinary Differential Equations of General Order. Matematičeskie zametki, Tome 76 (2004) no. 1, pp. 52-65. http://geodesic.mathdoc.fr/item/MZM_2004_76_1_a5/

[1] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1970

[2] Riordan D., Kombinatornye tozhdestva, Nauka, M., 1982 | Zbl

[3] Derevenskii V. P., “Reshenie sistem matrichnykh algebraicheskikh lineinykh uravnenii”, Izv. vuzov. Matem., 1998, no. 10 (437), 32–36 | MR | Zbl

[4] Dzhekobson N., Algebry Li, Mir, M., 1964

[5] Derevenskii V. P., “Matrichnye lineinye differentsialnye uravneniya vysshikh poryadkov”, Differents. uravneniya, 29:4 (1993), 711–714 | Zbl

[6] Derevenskii V. P., “Eksponentsialnoe reshenie matrichnykh lineinykh differentsialnykh uravnenii pervogo poryadka”, Izv. vuzov. Matem., 1981, no. 7, 31–33 | MR | Zbl

[7] Derevenskii V. P., “Sistemy matrichnykh lineinykh differentsialnykh uravnenii pervogo poryadka”, Matem. zametki, 66:1 (1999), 63–75 | MR | Zbl

[8] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967