Question

Find the general solution of the differential equation $\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}=0$.

Answer 1

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

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

Integrating both sides, we get

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