General form of a differential equation of order n (Q1998)

F\\!\\left(x_1,\\dots,x_m,\\;u,\\;\\frac{\\partial u}{\\partial x_1},\\dots,\\frac{\\partial u}{\\partial x_m},\\;\\frac{\\partial^2u}{\\partial x_1^2},\\dots,\\frac{\\partial^\\alpha u}{\\partial x_1^{\\alpha_1}\\cdots\\partial x_m^{\\alpha_m}},\\dots\\right)=0,\n\\qquad \\alpha=(\\alpha_1,\\dots,\\alpha_m)\\in\\mathbb N^m.