\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-3\,{x}^{2}y \left ( x \right ) +1+{x}^{6} \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{3}{x}^{9}}{{x}^{3}}}=0} \]
Mathematica: cpu = 0.063008 (sec), leaf count = 95 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 x^6 y(x)+x^3}{\sqrt [3]{29} \sqrt [3]{x^9}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1+\frac {29^{2/3} \left (x^9\right )^{2/3}}{9 x^5},y(x)\right ] \]
Maple: cpu = 0.031 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\frac {-3+29\,{\it RootOf} \left ( -81\, \int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}+x+3\,{\it \_C1} \right ) }{9\,{x}^{3}}} \right \} \]