\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {6\,x+{x}^{3}+{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}+4\,{x}^{2}y \left ( x \right ) +{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+6\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+12\,xy \left ( x \right ) +8}{{x}^{3}}}=0} \]
Mathematica: cpu = 0.048006 (sec), leaf count = 80 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 y(x)+\frac {x+6}{x}}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {1}{9} 29^{2/3} x,y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\frac {29\,{\it RootOf} \left ( -81\, \int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{\it \_C1} \right ) x-3\,x-18}{9\,x}} \right \} \]