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

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

$\Rightarrow$ $\frac{{dy}}{{dx}} = - \frac{{\sqrt {1 - {y^2}} }}{{\sqrt {1 - {x^2}} }}$
$\Rightarrow$ $\frac{{dy}}{{\sqrt {1 - {y^2}} }} = \frac{{ - dx}}{{\sqrt {1 - {x^2}} }}$
Integrating both sides,

we get:
${\sin ^{ - 1}}y = - {\sin ^{ - 1}}x + C$
$\Rightarrow$ ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = C$