The solution of \(\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = \sqrt {1 - {{\rm{x}}^2} - {{\rm{y}}^2} + {{\rm{x}}^2}{{\rm{y}}^2}} \) is

• A. sin-1 y = sin-1 x + c
• B. \(2{\sin ^{ - 1}}{\rm{y}} = \sqrt {1 - {{\rm{x}}^2}} + {\sin ^{ - 1}}{\rm{x}} + {\rm{c}}\)
• C. \(2{\sin ^{ - 1}}{\rm{y}} = {\rm{x}}\sqrt {1 - {{\rm{x}}^2}} + {\sin ^{ - 1}}{\rm{x}} + {\rm{c}}\)
• D. \(2{\sin ^{ - 1}}{\rm{y}} = {\rm{x\;}}\sqrt {1 - {{\rm{x}}^2}} + {\cos ^{ - 1}}{\rm{x}} + {\rm{c}}\)