A curve passes through the point (x = 1, y = 0) and satisfies the differential equation \(\frac{{{\rm{dy}}}}{{{\rm{dx}}}} = \frac{{{{\rm{x}}^2} + {{\rm{y}}^2}}}{{2{\rm{y}}}} + \frac{{\rm{y}}}{{\rm{x}}}.\) The equation that describes the curve is
1
\({\rm{ln}}\left( {1 + \frac{{{{\rm{y}}^2}}}{{{{\rm{x}}^2}}}} \right) = {\rm{x}} - 1\)
2
\(\frac{1}{2}{\rm{ln}}\left( {1 + \frac{{{{\rm{y}}^2}}}{{{{\rm{x}}^2}}}} \right) = {\rm{x}} - 1\)
3
\({\rm{ln}}\left( {1 + \frac{{\rm{y}}}{{\rm{x}}}} \right) = {\rm{x}} - 1\)
4
\(\frac{1}{2}{\rm{ln}}\left( {1 + \frac{{\rm{y}}}{{\rm{x}}}} \right) = {\rm{x}} - 1\)