Question

The differential equation for which ${\sin }^{-1}x+{\sin }^{-1}y=c$ is given by:

• A. $\sqrt{1-x^2}dy+\sqrt{1-y^2}dx=0$
• B. $\sqrt{1-x^2}dx+\sqrt{1-y^2}dy=0$
• C. $\sqrt{1-x^2}dx-\sqrt{1-y^2}dy=0$
• D. $\sqrt{1-x^2}dy-\sqrt{1-y^2}dx=0$

Answer 1

The correct option is A $\sqrt{1-x^2}dy+\sqrt{1-y^2}dx=0$

Given, ${\sin }^{-1}x+{\sin }^{-1}y=c$

Differentiating both sides, we get

$\frac{dx}{\sqrt{1-x^2}}+\frac{dy}{\sqrt{1-y^2}}=0$

$\Rightarrow \sqrt{1-x^2}dy+\sqrt{1-y^2}dx=0$