The correct answer is Option D. To find the Integrating Factor, first rewrite the given differential equation in standard linear form. The given equation is $(1 - y^2) \frac{dx}{dy} + yx = ay$. Dividing both sides by $(1 - y^2)$, we get $\frac{dx}{dy} + \frac{y}{1-y^2}x = \frac{ay}{1-y^2}$. This is of the form $\frac{dx}{dy} + Px = Q$ where $P = \frac{y}{1-y^2}$. The Integrating Factor is $e^{\int P \, dy} = e^{\int \frac{y}{1-y^2} \, dy}$. Using substitution $u = 1-y^2$, we get $du = -2y \, dy$, so the integral becomes $-\frac{1}{2}\ln(1-y^2)$. Therefore, I.F. $= e^{-\frac{1}{2}\ln(1-y^2)} = (1-y^2)^{-1/2} = \frac{1}{\sqrt{1-y^2}}$. Since $-1 < y < 1$, the expression $1-y^2$ is positive, making the square root well-defined.