Integrating factor of the differential equation $\left(1-y^2\right) \frac{dx}{dy}+x y=a y$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - $\frac{1}{\sqrt{1-y^2}}$
I.F. = ?
dividing eq. by $1-y^2$
so $\frac{dx}{dy}+\frac{y}{1-y^2}x=\frac{ay}{1-y^2}$
$I.F.=e^{\int\frac{y}{1-y^2}}dy=e^{-\frac{1}{2}\int\frac{-2y}{1-y^2}}dy$
$=e^{-\frac{1}{2}\log 1-y^2}=\frac{1}{\sqrt{1-y^2}}$