General solution of $\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}=0$ is :
Answer & explanation
Correct answer: option 1
Given differential equation:
$\frac{dy}{dx} + \sqrt{\frac{1-y^2}{1-x^2}} = 0$
$\Rightarrow \frac{dy}{dx} = -\sqrt{\frac{1-y^2}{1-x^2}}$
Separating variables:
$\frac{dy}{\sqrt{1-y^2}} = -\frac{dx}{\sqrt{1-x^2}}$
Integrating both sides:
$\sin^{-1}y = -\sin^{-1}x + C$
final answer: The general solution is $\sin^{-1}y + \sin^{-1}x = C$