Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University444810.18287/2541-7525-2015-21-10-40-46On conditions of solvability of three-dimensional integralsystem in quadraturesSozontovaE.A.morenov.sv@ssau.ru15102015211040461505201715052017Copyright © 2015, Sozontova E.2015In 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.partial integral system, condition of solvability, solution in quadratures, differential equation, Goursat problem.система с частными интеграламиусловие разреши- мостирешение в квадратурахдифференциальное уравнениезадача Гурса