  We study the dynamics of a two-qubit system coupled through time dependent
anisotropic $XYZ$ Heisenberg interaction in presence of a time varying
non-uniform external magnetic field. Exact results are presented for the time
evolution of the system under certain integrability conditions. Furthermore,
the corresponding entanglement of the system is studied for different values of
the involved parameters. We found that the time evolution and different
properties of entanglement such as amplitude, frequency and profile can be
finely tuned by the interplay of the characteristics of the time-dependent
magnetic field and exchange coupling. Also we show how the discrete symmetries
of the system Hamiltonian, which splits its Hilbert space into two distinct
subspaces, can be utilized to deduce the dynamics in one of its two distinct
subspaces from the other one. Moreover, approximate results for the time
evolution are provided utilizing the rotating wave as well as the perturbation
approximations for the special case of either static magnetic field or exchange
coupling. We compare the range of validity of the two approximation methods and
their effectiveness in treating the considered system and determine their
critical parameters.
