Integrating factor of the differential equation $\left(1-y^2\right) \frac{dx}{dy}+x y=a y$ is:

$\frac{1}{1-y^2}$ $\frac{1}{\sqrt{y^2-1}}$ $\frac{1}{y^2-1}$ $\frac{1}{\sqrt{1-y^2}}$

$\frac{1}{\sqrt{1-y^2}}$

The correct answer is Option (4) - $\frac{1}{\sqrt{1-y^2}}$