\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-2\,x-y \left ( x \right ) +1+{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{3}y \left ( x \right ) +{x}^{4}+{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+3\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+3\,{x}^{5}y \left ( x \right ) +{x}^{6}}{x}}=0} \]
Mathematica: cpu = 0.057507 (sec), leaf count = 98 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 x^3+3 x^2 y(x)+x}{\sqrt [3]{29} \sqrt [3]{x^3}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {29^{2/3} \left (x^3\right )^{2/3}}{9 x},y(x)\right ] \]
Maple: cpu = 0.016 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={\frac {-9\,{x}^{2}+29\,{\it RootOf} \left ( -81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{\it \_C1} \right ) -3}{9\,x}} \right \} \]