The general solution of the differential equation $\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}=0$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $sin^{-1}x+sin^{-1}y=C$ (where C is constant of integration)
$\frac{dy}{dx}=-\sqrt{\frac{1-y^2}{1-x^2}}$
$⇒\int\frac{1}{\sqrt{1-y^2}}dy=\int\frac{-dx}{\sqrt{1-x^2}}$
so $\sin^{-1}y=\sin^{-1}x×(-1)+C$
so $\sin^{-1}x+\sin^{-1}y=C$