= Solution
Split the microscopic sources into free and bound parts and define
$$
D=\epsilon_0E+P,
\qquad
H=\frac{B}{\mu_0}-M.
$$
Substitution of $\rho=\rho_{\rm f}-\nabla\cdot P$ into <Gauss's law> gives $\nabla\cdot D=\rho_{\rm f}$. Similarly, using $J=J_{\rm f}+\partial_tP+\nabla\times M$ in the <Ampère-Maxwell equation> gives $\nabla\times H=J_{\rm f}+\partial_tD$. The homogeneous <Maxwell equations> are unchanged. Thus
$$
\nabla\cdot D=\rho_{\rm f},\qquad
\nabla\times H=J_{\rm f}+\frac{\partial D}{\partial t},
$$
$$
\nabla\cdot B=0,\qquad
\nabla\times E=-\frac{\partial B}{\partial t}.
$$
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