\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {2\,{x}^{2}-4\,{x}^{3}y \left ( x \right ) +1+{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{6} \left ( y \left ( x \right ) \right ) ^{3}-3\, \left ( y \left ( x \right ) \right ) ^{2}{x}^{5}+3\,y \left ( x \right ) {x}^{4}-{x}^{3}}{{x}^{4}}}=0} \]
Mathematica: cpu = 0.054507 (sec), leaf count = 82 \[ \text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 x^2 y(x)-3 x+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=c_1-\frac {29^{2/3}}{9 x},y(x)\right ] \]
Maple: cpu = 0.016 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={\frac {9\,x-3+29\,{\it RootOf} \left ( - 81\,\int ^{{\it \_Z}}\! \left ( 841\,{{\it \_a}}^{3}-27\,{\it \_a}+27 \right ) ^{-1}{d{\it \_a}}x+3\,x{\it \_C1}-1 \right ) }{9\,{x}^{2}}} \right \} \]