\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-{x}^{2}+x+1+ \left ( y \left ( x \right ) \right ) ^{2}+5\,{x}^{2}y \left ( x \right ) -2\,xy \left ( x \right ) +4\,{x}^{4}-3\,{x}^{3}+ \left ( y \left ( x \right ) \right ) ^{3}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-3\,x \left ( y \left ( x \right ) \right ) ^{2}+3\,y \left ( x \right ) {x}^{4}-6\,{x}^{3}y \left ( x \right ) +{x}^{6}-3\,{x}^{5}}{x}}=0} \]
Mathematica: cpu = 0.063008 (sec), leaf count = 108 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {\frac {3 x^2-3 x+1}{x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x),y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =-{x}^{2}+x-{\frac {1}{3}}+{\frac {29\,{ \it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3 }-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+\ln \left ( x \right ) +3 \,{\it \_C1} \right ) }{9}} \right \} \]