The 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) : $sin^{-1} x + sin^{-1} y = C$
We have,
$\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}=0$
$⇒\frac{1}{\sqrt{1-y^2}}dy+\frac{1}{\sqrt{1-x^2}}dx=0$
On integrating, wehave
$sin^{-1} x + sin^{-1} y = C$