\[ \boxed { \left ( {x}^{2}+1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( 2\,xy \left ( x \right ) -1 \right ) =0} \]
Mathematica: cpu = 0.420553 (sec), leaf count = 203 \[ \text {Solve}\left [c_1=\frac {\frac {1}{2} \left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right ) \sqrt [4]{1-\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2} \, _2F_1\left (\frac {1}{2},\frac {5}{4};\frac {3}{2};\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2\right )+i x}{\sqrt [4]{-1+\left (\frac {1}{\frac {i x}{x^2+1}-\frac {i x^2 y(x)}{x^2+1}}+\frac {i}{x}\right )^2}},y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 85 \[ \left \{ {\it \_C1}+{x{\frac {1}{\sqrt [4]{ \left ( {x}^{-1}+{{x}^{2} \left ( {\frac {y \left ( x \right ) {x}^{4}}{{x}^{2}+1}}-{\frac {{x}^{3 }}{{x}^{2}+1}} \right ) ^{-1}} \right ) ^{2}+1}}}}+{\frac {y \left ( x \right ) +x}{2\,xy \left ( x \right ) -2} {\mbox {$_2$F$_1$}({\frac {1}{2}},{\frac {5}{4}};\,{\frac {3}{2}};\,-{\frac { \left ( y \left ( x \right ) +x \right ) ^{2}}{ \left ( xy \left ( x \right ) -1 \right ) ^{2}}})} }=0 \right \} \]