⁶Tricks or knowledge. If $D$ is a constant, the particular solution $x_{\mathit{particular}}=\mathit{constant}$ can be tried. The same goes for $D=\mathit{sin}(\mathit{\omega t})$ where $x_{\mathit{particular}}=A\cdot \mathit{sin}(\mathit{\omega t})+B\cdot \mathit{cos}(\mathit{\omega t})$ can be tried.