Question

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

• A. ${\sin }^{-1}y-{\sin }^{-1}x=C$
• B. ${\sin }^{-1}y+{\sin }^{-1}x=C$
• C. ${\sin }^{-1}(xy)=2$
• D. None of these

Answer 1

Answer: (A)

Given, $\frac{dy}{\sqrt{1-y^2}}=\frac{dx}{\sqrt{1-x^2}}$
Integrating both sides, we get
$si{n}^{-1}y=si{n}^{-1}x+C$
or $si{n}^{-1}y=si{n}^{-1}x=C$.