1. **Problem:** Solve the differential equation $$(D^3 + 3D^2 + 3D + 1) y = 0$$ where $D = \frac{d}{dx}$. 2. **Characteristic equation:** Replace $D$ by $r$ to get $$r^3 + 3r^2 + 3r + 1 = 0$$ 3. **Recognize the pattern:** This is a perfect cube expansion: $$r^3 + 3r^2 + 3r + 1 = (r + 1)^3 = 0$$ 4. **Roots:** The root is $r = -1$ with multiplicity 3. 5. **General solution:** For repeated roots $r$ of multiplicity $m$, the solution is $$y = (C_1 + C_2 x + C_3 x^2) e^{rx}$$ 6. **Apply roots:** Here, $$y = (C_1 + C_2 x + C_3 x^2) e^{-x}$$ **Final answer:** $$\boxed{y = (C_1 + C_2 x + C_3 x^2) e^{-x}}$$