General implicit form of a partial differential equation (Q1604)

F\\Bigl(x_1,x_2,\\ldots,x_n,\\ u,\\ \\frac{\\partial u}{\\partial x_1},\\ldots,\\ \\frac{\\partial^{2}u}{\\partial x_i\\,\\partial x_j},\\ldots\\Bigr)=0