  The study of integrability of the mathematical physics equations showed that
the differential equations describing real processes are not integrable without
additional conditions. This follows from the functional relation that is
derived from these equations. Such a relation connects the differential of
state functional and the skew-symmetric form. This relation proves to be
nonidentical, and this fact points to the nonintegrability of the equations. In
this case a solution to the equations is a functional, which depends on the
commutator of skew-symmetric form that appears to be unclosed. However, under
realization of the conditions of degenerate transformations, from the
nonidentical relation it follows the identical one on some structure. This
points out to the local integrability and realization of a generalized
solution.
  In doing so, in addition to the exterior forms, the skew-symmetric forms,
which, in contrast to exterior forms, are defined on nonintegrable manifolds
(such as tangent manifolds of differential equations, Lagrangian manifolds and
so on), were used.
  In the present paper, the partial differential equations, which describe any
processes, the systems of differential equations of mechanics and physics of
continuous medium and field theory equations are analyzed.
