Geodesic
On conditions of solvability of three-dimensional integral system in quadratures
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 40-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.
Keywords: partial integral system, condition of solvability, differential equation
Mots-clés : solution in quadratures, Goursat problem. 
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E. A. Sozontova. On conditions of solvability of three-dimensional integral system in quadratures. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2015), pp. 40-46. http://geodesic.mathdoc.fr/item/VSGU_2015_10_a3/

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