The integrating factor of the differential equation $(1 - y^2) \frac{dx}{dy} + yx = ay, (-1 < y < 1)$ is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{\sqrt{1 - y^2}}$ ##
The given differential equation is
$(1 - y^2) \frac{dx}{dy} + yx = ay, (-1 < y < 1)$
Rewrite the differential equation:
$\frac{dx}{dy} + \frac{yx}{(1-y^2)} = \frac{ay}{(1-y^2)}$
The integrating factor is $e^{\int \frac{y}{1-y^2} dy}$
$= e^{-\frac{1}{2} \log |1-y^2|}$
$= \frac{1}{\sqrt{1-y^2}}$