In the presented report, the theory of E. Cartan’s invariants of multidimensional Riemann metrics related to non-linear differential equations, which have important applications in various areas of modern mathematical physics, will be considered in order to construct their exact solutions. As examples, we consider a 6-dimensional space with the metric 6ds2 = 4Uxpdxdt+4Uypdydt+(−2pUUx−2pUxxx−2μqUy+2UUx)dt2+ +2dxdp + 2dydq + dUdt, that is Ricci-flat on solutions of the well-known Kadomtsev-Petviashvili equation (Ux)2 + UUxx + Uxxxx + Uxt + μUyy = 0 and the 14-dimensional Ricci-flat metric on solutions of the NavierStokes system of equations, describing the motion of an incompressible viscous fluid [1].For build new examples of solutions of indicated differential equations the Invariants of E.Cartan [2] S = R(i ajb)R(j cid)kakbkckd, T = R(i ajb;cd)R(j eif;gh)kakbkckd kekfkgkh. and Q = R(ab)R(cd)kakbkckd, where R(j cid) and R(cd) are the tensor of Riemann and Ricci-tensor of metric, kq -components of vector field are applied and their properties are discussed.