$x{y^\prime } = {\left( {1 - {y^2}} \right)^{1/2}}.$
$\qquad$$\qquad$$\therefore Separable$
$\qquad$$\qquad$$\therefore x \frac{d y}{d x}=\sqrt{1-y^{2}}$
$\qquad$$\qquad$$Rearrange:~\int \frac{1}{\sqrt{1-y^{2}}} d y=\int \frac{1}{x} d x \quad~where~x \neq 0, y \neq \pm 1$
$\qquad\qquad {Integrating on both side}:$
$\qquad\qquad LHS:\int \frac{1}{\sqrt{1-y^{2}}}=\arcsin y=\ln |y|+C$
$\qquad\qquad RHS:\int \frac{1}{x} d x=\ln |x|$
$\qquad\qquad \therefore~General~sol:\arcsin y=\ln|x|+C$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad y=\sin ( \ln |x |+C) \quad x \neq 0 \quad y \neq \pm 1$
