\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-3\,{x}^{2}y \left ( x \right ) -2\,{x}^{3}-2\,x-x \left ( y \left ( x \right ) \right ) ^{2}-y \left ( x \right ) +{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+3\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+3\,{x}^{5}y \left ( x \right ) +{x}^{6}}{x \left ( xy \left ( x \right ) +{x}^{2}+1 \right ) }}=0} \]
Mathematica: cpu = 0.027003 (sec), leaf count = 80 \[ \left \{\left \{y(x)\to \frac {1}{x^2 \left (\frac {1}{x}-\frac {1}{x \sqrt {c_1-2 x}}\right )}-\frac {x^2+1}{x}\right \},\left \{y(x)\to \frac {1}{x^2 \left (\frac {1}{x \sqrt {c_1-2 x}}+\frac {1}{x}\right )}-\frac {x^2+1}{x}\right \}\right \} \]
Maple: cpu = 0.032 (sec), leaf count = 73 \[ \left \{ y \left ( x \right ) =-{\frac {1}{x} \left ( \sqrt {{\it \_C1}-2 \,x}{x}^{2}-{x}^{2}-1 \right ) \left ( \sqrt {{\it \_C1}-2\,x}-1 \right ) ^{-1}},y \left ( x \right ) =-{\frac {1}{x} \left ( \sqrt {{\it \_C1}-2\,x}{x}^{2}+{x}^{2}+1 \right ) \left ( \sqrt {{\it \_C1}-2\,x}+1 \right ) ^{-1}} \right \} \]