The given differential equation is \(\sqrt{1-y^2}\)

\(\Rightarrow x \frac{dy}{dx}= \sqrt{1-y^2}\)

\(\Rightarrow \frac{1}{\sqrt{1-y^2}} dy= \frac{dx}{x}\)

Integrating both sides, we obtain

\(\int \frac{1}{\sqrt{1-y^2}} dy=\int \frac{dx}{x}\)

\(\Rightarrow sin^{-1}(y)= ln (|x|)+c\)

\(\Rightarrow y= \sin (ln(|x|)+c)\)

\(\Rightarrow x \frac{dy}{dx}= \sqrt{1-y^2}\)

\(\Rightarrow \frac{1}{\sqrt{1-y^2}} dy= \frac{dx}{x}\)

Integrating both sides, we obtain

\(\int \frac{1}{\sqrt{1-y^2}} dy=\int \frac{dx}{x}\)

\(\Rightarrow sin^{-1}(y)= ln (|x|)+c\)

\(\Rightarrow y= \sin (ln(|x|)+c)\)