= Solution
Substitution of the sinusoidal <plane electromagnetic wave>[plane waves] into <Faraday's law> gives
$$
\mathbf k\times\mathbf e=\omega\mathbf b.
$$
The source-free <Ampère-Maxwell equation>, with $\mathbf H=\mathbf B/\mu$ and $D_i=\varepsilon_{ij}E_j$, gives
$$
\mathbf k\times\frac{\mathbf b}{\mu}
=-\omega\boldsymbol\varepsilon\mathbf e.
$$
Eliminating $\mathbf b=(\mathbf k\times\mathbf e)/\omega$ yields the wave equation for a <plane wave in an anisotropic dielectric>:
$$
\boxed{
[\mathbf k\times(\mathbf k\times\mathbf e)]_i
+\omega^2\mu\varepsilon_{ij}e_j=0}.
$$
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