\[ y'(x)=\frac {(x y(x)+1)^3}{x^5} \] ✓ Mathematica : cpu = 0.193417 (sec), leaf count = 124
\[\text {Solve}\left [6 \left (c_1+\left (-\frac {1}{x^6}\right )^{5/3} x^9\right )+\log \left (-\sqrt [3]{-\frac {1}{x^6}} (x y(x)+1)^2+\left (-\frac {1}{x^6}\right )^{2/3} x^3 (x y(x)+1)+1\right )=2 \left (\sqrt {3} \tan ^{-1}\left (\frac {2 \left (-\frac {1}{x^6}\right )^{5/3} x^9 (x y(x)+1)-1}{\sqrt {3}}\right )+\log \left (\frac {x y(x)+1}{\sqrt [3]{-\frac {1}{x^6}} x^3}+1\right )\right ),y(x)\right ]\]
✓ Maple : cpu = 3.673 (sec), leaf count = 86
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}}{6\,x} \left ( 3\,\tan \left ( {\it RootOf} \left ( -18\,{x}^{3} \left ( -{x}^{-6} \right ) ^{2/3}-6\,{\it \_Z}\,\sqrt {3}-\ln \left ( {\frac { \left ( \sqrt {3}+\tan \left ( {\it \_Z} \right ) \right ) ^{6}}{ \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) ^{3}}} \right ) +18\,{\it \_C1} \right ) \right ) {x}^{3}\sqrt [3]{-{x}^{-6}}+\sqrt {3} \left ( {x}^{3}\sqrt [3]{-{x}^{-6}}-2 \right ) \right ) } \right \} \]