“[...] the general solution of a given
deterministic system in involution depends on arbitrary functions of three variables in the sense
that the 3-dimensional solution (
) that
determines the most general solution can be obtained by arbitrarily
taking
of the unknown functions to be
functions of
.”
Here, is the number of equations of
the system for
unknown functions;
denotes the number of existing linear relations
among the
derivatives of the unknowns with regard
to two arbitrary directions in 3-space.