Modeling by means of differential equations is considered in the paper. Their solutions are constructed on the base of functional relations connecting values of a solution of the equation in different points (infinite or finite set of values). For examples, even, odd and periodical solutions, Vallée-Poussin’s assertion, Lagrange interpolation polynomial, Hermite interpolation polynomial, spline-functions for ordinary differential equations, Asgeirsson’s identity and its generalizations for partial differential equations of hyperbolic type, “mean value” for partial differential equations of elliptic type are considered. Also, if an equation is close to one of considered types then an assertion is to be fulfilled approximately. Some estimations are found for such examples. An application of such relations to investigate some problems of interpolation and extrapolation is demonstrated.