Q. The solution of $\frac{dy}{dx} + \sqrt{\left( \frac{1 - y^{2}}{1 - x^{2}} \right)} = 0$ is
A) $\tan^{- 1}x + \cot^{- 1}x = c$
B) $\sin^{- 1}x + \sin^{- 1}y = c$
C) $\sec^{- 1}x + cosec^{- 1}x = c$
D) None of these
Explanation
(b)
Given, $\frac{dy}{dx} + \sqrt{\frac{1 - y^{2}}{1 - x^{2}}} = 0$
$\Rightarrow$ $\int_{}^{}\frac{dy}{\sqrt{1 - y^{2}}} + \int_{}^{}\frac{dx}{\sqrt{1 - x^{2}}} = 0$
$\Rightarrow$ $\sin^{- 1}x + \sin^{- 1}y = c\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.