Explicit differential characterization of PDE systems pointwise equivalent to Y_(X^(j₁)X^(j₂))=0, 1leq j₁,j₂leq ngeq 2

In this paper, a direct continuation of math.DG/0411165, we generalize S. Lie's linearization criterion of an ordinary second order differential equation to the case of several independent variables (x^1, x^2 ..., x^n), n >1, and a single dependent variable y. Strikingly, as in math.DG/0411165, the (complicated) characterizing differential system is of first order. By means of computer programming, this phenomenon was discovered in the case n=2 by S. Neut and M. Petitot (www.lifl.fr/~neut/recherche/these.pdf).