1. **State the problem:** We need to form a differential equation from the given implicit relation $$y^2 = (x+c)^3$$ where $c$ is a constant. 2. **Rewrite the equation:** The equation is $$y^2 = (x+c)^3$$. 3. **Differentiate both sides with respect to $x$:** Using implicit differentiation, $$\frac{d}{dx}(y^2) = \frac{d}{dx}((x+c)^3)$$ 4. **Apply the chain rule:** $$2y \frac{dy}{dx} = 3(x+c)^2 \cdot 1$$ 5. **Express $(x+c)^2$ in terms of $y$:** From the original equation, $$y^2 = (x+c)^3 \implies (x+c) = y^{2/3}$$ so $$(x+c)^2 = (y^{2/3})^2 = y^{4/3}$$ 6. **Substitute back:** $$2y \frac{dy}{dx} = 3 y^{4/3}$$ 7. **Simplify:** $$\frac{dy}{dx} = \frac{3 y^{4/3}}{2y} = \frac{3}{2} y^{1/3}$$ 8. **Final differential equation:** $$\frac{dy}{dx} = \frac{3}{2} y^{1/3}$$ This is the differential equation formed from the given implicit relation.