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Mathematics Question on integral

The solution of the equation dydx=1−y21−x2\frac{dy}{dx}=\sqrt\frac{1-y^2}{1-x^2} is

A

sin⁡−1y−sin⁡−1x=C\sin^{-1}y -\sin^{-1} x = C

B

sin⁡−1y+sin⁡−1x=C\sin^{-1} y + \sin^{-1} x = C

C

sin⁡−1(xy)=2\sin^{-1} (xy) = 2

D

None of these

Answer

sin⁡−1y−sin⁡−1x=C\sin^{-1}y -\sin^{-1} x = C

Explanation

Solution

Given, dy1−y2=dx1−x2\frac{dy}{\sqrt{1-y^{2}}} = \frac{dx}{\sqrt{1-x^{2}}} Integrating both sides, we get sin−1 y=sin−1 x+Csin^{-1}\, y = sin^{-1}\, x + C or sin−1 y=sin−1 x=Csin^{-1}\, y = sin^{-1}\, x = C.