1. The problem asks to determine the order of the given differential equation. 2. The given differential equation is $$(1-x^2) \frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + n(n+1) y = 0$$ 3. The order of a differential equation is defined as the order of the highest derivative present in the equation. 4. Here, the highest derivative is $$\frac{d^2 y}{dx^2}$$ which is the second derivative of $$y$$ with respect to $$x$$. 5. Therefore, the order of this differential equation is two. **Final Answer:** Option a. order two