\[ y'(x)=\frac {(x y(x)+1)^3}{x^5} \] ✓ Mathematica : cpu = 0.205106 (sec), leaf count = 157
\[\text {Solve}\left [\frac {1}{3} \log \left (\frac {\frac {3 y(x)}{x^2}+\frac {3}{x^3}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )-\frac {1}{6} \log \left (\frac {\left (\frac {3 y(x)}{x^2}+\frac {3}{x^3}\right )^2}{9 \left (-\frac {1}{x^6}\right )^{2/3}}-\frac {\frac {3 y(x)}{x^2}+\frac {3}{x^3}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 \left (\frac {3 y(x)}{x^2}+\frac {3}{x^3}\right )}{3 \sqrt [3]{-\frac {1}{x^6}}}-1}{\sqrt {3}}\right )}{\sqrt {3}}=-\left (-\frac {1}{x^6}\right )^{2/3} x^3+c_1,y(x)\right ]\] ✓ Maple : cpu = 1.2 (sec), leaf count = 86
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}}{6\,x} \left ( 3\,\tan \left ( {\it RootOf} \left ( -18\,{x}^{3} \left ( -{x}^{-6} \right ) ^{2/3}-6\,\sqrt {3}{\it \_Z}-\ln \left ( {\frac { \left ( \sqrt {3}+\tan \left ( {\it \_Z} \right ) \right ) ^{6}}{ \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) ^{3}}} \right ) +18\,{\it \_C1} \right ) \right ) {x}^{3}\sqrt [3]{-{x}^{-6}}+\sqrt {3} \left ( {x}^{3}\sqrt [3]{-{x}^{-6}}-2 \right ) \right ) } \right \} \]