Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8282Symbolic Solving of Diﬀerential Equations with Partial DerivativesMalaschonokN ATambov State Universitynamalaschonok@gmail.comTambov State University020220102.2101408092016Copyright © 2010,2010An algorithm for the symbolic solving of systems of linear partial diﬀerential equations by means of multivariate Laplace-Carson transform (LC) is produced. Considered is a system of K linear equations with M as the greatest order of partial derivatives and right hand parts of a special type, that permits a symbolic Laplace-Carson transform. Initial conditions are input. As a result of Laplace-Carson transform of the system according to the initial conditions, we obtain an algebraic system of equations. There exist eﬃcient methods to solve large size systems of such types. It gives a possibility to implement the method for solving the large PDE systems. A method to obtain compatibility conditions is discussed. The application of LC allows one to execute it in a symbolic way.systems of partial diﬀerential equationsLaplace-Carson transformsymbolic solvingсистемы дифференциальных уравнений в частных производныхпреобразование Лапласа-Карсонасимвольное решение