  The equations for the general Darboux-Halphen system obtained as a reduction
of the self-dual Yang-Mills can be transformed to a third-order system which
resembles the classical Darboux-Halphen system with a common additive terms. It
is shown that the transformed system can be further reduced to a constrained
non-autonomous, non-homogeneous dynamical system. This dynamical system becomes
homogeneous for the classical Darboux-Halphen case, and was studied in the
context of self-dual Einstein's equations for Bianchi IX metrics. A Lax pair
and Hamiltonian for this reduced system is derived and the solutions for the
system are prescribed in terms of hypergeometric functions.
