A universal solution

The phenomenon of an implicit function which solves a large set of second order partial differential equations obtainable from a variational principle is explicated by the introduction of a class of universal solutions to the equations derivable from an arbitrary Lagrangian which is homogeneous of weigh one in the field derivatives. This result is extended to many fields. The imposition of Lorenz invariance makes such Lagrangians unique, and equivalent to the Companion Lagrangians introduced in [1].