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