  We study the groups of local BRST cohomology associated to the general
systems of ordinary differential equations, not necessarily Lagrangian or
Hamiltonian. Starting with the involutive normal form of the equations, we
explicitly compute certain cohomology groups having clear physical meaning.
These include the groups of global symmetries, conservation laws and Lagrange
structures. It is shown that the space of integrable Lagrange structures is
naturally isomorphic to the space of weak Poisson brackets. The last fact
allows one to establish a direct link between the path-integral quantization of
general not necessarily variational dynamics by means of Lagrange structures
and the deformation quantization of weak Poisson brackets.
