Q223 / 270 · NDA 2011 (Phase 1) · Mathematics
What is the solution of the differential equation
$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0 ?$
where $c$ is a constant.
- Correct answerA$\sin ^{-1} y+\sin ^{-1} x=c$
- B$\sin ^{-1} y-\sin ^{-1} x=c$
- C$2 \sin ^{-1} y+\sin ^{-1} x=c$
- D$2 \sin ^{-1} y-\sin ^{-1} x=c$
Solution
$\frac{d y}{\sqrt{1+y^2}}+\frac{d x}{\sqrt{1-x_2}}=0$
on integration
$\sin ^{-1} y+\sin ^{-1} x=C$
Hence, the correct answer is option: 'A'.