  Further investigations of implicit solutions to non-linear partial
differential equations are pursued. Of particular interest are the equations
which are Lorentz invariant. The question of which differential equations of
second order for a single unknown $\phi$ are solved by the imposition of an
inhomogeneous quadratic relationship among the independent variables, whose
coefficients are functions of $\phi$ is discussed, and it is shown that if the
discriminant of the quadratic vanishes, then an implicit solution of the
so-called Universal Field Equation is obtained. The relation to the general
solution is discussed.
