= Solution
Comparison with the <multivariate normal density> shows that $D$ is its <precision matrix>. Since the mean is zero,
$$
\boxed{C_{ij}=\langle x_ix_j\rangle=(D^{-1})_{ij}.}
$$
Multiplying $a+\frac12bD=0$ on the right by $C=D^{-1}$ gives $aC=-b/2$. Taking the transpose and using the symmetry of $b$ and $C$ gives $Ca^T=-b/2$. Hence the stationary covariance obeys the <Continuous Lyapunov equation>
$$
\boxed{aC+Ca^T+b=0.}
$$
The same equation follows directly by setting the time derivative of the second-moment equation from part (c) to zero.
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