  The density dependence of the symmetry energy in the equation of state of
isospin asymmetric nuclear matter is studied using the isoscaling of the
fragment yields and the antisymmetrized molecular dynamic calculation. It is
observed that the experimental data at low densities are consistent with the
form of symmetry energy,E$_{sym}$ $\approx$ 31.6 ($\rho/\rho_{\circ})^{0.69}$,
in close agreement with those predicted by the results of variational many-body
calculation. A comparison of the present result with those reported recently
using the NSCL-MSU data suggests that the heavy ion studies favor a dependence
of the form, E$_{sym}$ $\approx$ 31.6 ($\rho/\rho_{\circ})^{\gamma}$, where
$\gamma$ = 0.6 - 1.05. This constraints the form of the density dependence of
the symmetry energy at higher densities, ruling out an extremely " stiff " and
" soft " dependences.
