\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,x+1+ \left ( y \left ( x \right ) \right ) ^{2}-2\,{x}^{2}y \left ( x \right ) +{x}^{4}+ \left ( y \left ( x \right ) \right ) ^{3}-3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+3\,y \left ( x \right ) {x}^{4}-{x}^{6}=0} \]
Mathematica: cpu = 0.042005 (sec), leaf count = 79 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {-3 x^2+3 y(x)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 28 \[ \left \{ y \left ( x \right ) ={x}^{2}+{\it RootOf} \left ( -x+\int ^{{ \it \_Z}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{ \it \_a}}+{\it \_C1} \right ) \right \} \]