The general solution of the DE dy/dx ​​​​​​(√(1 -x^2)) ((1 - y^2)) is

Question

The general solution of the DE \(\frac{dy}{dx}\) = \((\sqrt {1 - x^2)} (\sqrt {1 - y^2)}\) is 

A. sin^-1 y - sin^-1 x = x √(1 - x² ) + C

B. 2 sin^-1 y - sin^-1 x = x √(1 - x² ) + C

C. 2 sin^-1 y - sin^-1 x = C

D. None of these

Answer 1

Let x = sin t

dx = cos t dt

On integrating on both sides we get

Conclusion: Therefore,  is the solution of