The density dependence of the symmetry energy in the equation of state ofisospin asymmetric nuclear matter is studied using the isoscaling of thefragment yields and the antisymmetrized molecular dynamic calculation. It isobserved that the experimental data at low densities are consistent with theform 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-bodycalculation. A comparison of the present result with those reported recentlyusing the NSCL-MSU data suggests that the heavy ion studies favor a dependenceof 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 ofthe symmetry energy at higher densities, ruling out an extremely " stiff " and" soft " dependences.
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