Integrable Systems of Linear Ordinary Differential Equations of General Order

V. P. Derevenskii

Kazan State Academy of Architecture and Construction

Abstract: 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.

UDC: 517.9

Received: 20.05.2002

DOI: 10.4213/mzm86

 English version: Mathematical Notes, 2004, 76:1, 48–61

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