\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{x}^{2}y \left ( x \right ) +{x}^{4}+2\,{x}^{3}-3\,{x}^{2}+xy \left ( x \right ) +x+ \left ( y \left ( x \right ) \right ) ^{3}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-3\,x \left ( y \left ( x \right ) \right ) ^{2}+3\,y \left ( x \right ) {x}^{4}-6\,{x}^{3}y \left ( x \right ) +{x}^{6}-3\,{x}^{5}}{x \left ( y \left ( x \right ) +{x}^{2}-x+1 \right ) }}=0} \]
Mathematica: cpu = 0.021003 (sec), leaf count = 76 \[ \left \{\left \{y(x)\to \frac {1}{x \left (\frac {1}{x}-\frac {1}{x \sqrt {c_1-2 \log (x)}}\right )}-x^2+x-1\right \},\left \{y(x)\to \frac {1}{x \left (\frac {1}{x \sqrt {c_1-2 \log (x)}}+\frac {1}{x}\right )}-x^2+x-1\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) =-{1 \left ( \sqrt {{\it \_C1}-2\,\ln \left ( x \right ) }{x}^{2}-\sqrt {{\it \_C1}-2\,\ln \left ( x \right ) }x-{x}^{2}+x-1 \right ) \left ( -1+\sqrt {{\it \_C1}-2\,\ln \left ( x \right ) } \right ) ^{-1}},y \left ( x \right ) =-{1 \left ( \sqrt {{\it \_C1}-2\,\ln \left ( x \right ) }{x}^{2}-\sqrt {{\it \_C1}-2\,\ln \left ( x \right ) }x+{x}^{2}-x+1 \right ) \left ( 1+\sqrt {{\it \_C1}-2 \,\ln \left ( x \right ) } \right ) ^{-1}} \right \} \]