\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( xy \left ( x \right ) +1 \right ) ^{3}}{{x}^{5}}}=0} \]
Mathematica: cpu = 0.101013 (sec), leaf count = 157 \[ \text {Solve}\left [\frac {1}{3} \log \left (\frac {\frac {3}{x^3}+\frac {3 y(x)}{x^2}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )-\frac {1}{6} \log \left (\frac {\left (\frac {3}{x^3}+\frac {3 y(x)}{x^2}\right )^2}{9 \left (-\frac {1}{x^6}\right )^{2/3}}-\frac {\frac {3}{x^3}+\frac {3 y(x)}{x^2}}{3 \sqrt [3]{-\frac {1}{x^6}}}+1\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 \left (\frac {3}{x^3}+\frac {3 y(x)}{x^2}\right )}{3 \sqrt [3]{-\frac {1}{x^6}}}-1}{\sqrt {3}}\right )}{\sqrt {3}}=c_1-\left (-\frac {1}{x^6}\right )^{2/3} x^3,y(x)\right ] \]
Maple: cpu = 0.187 (sec), leaf count = 88 \[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}}{6\,x} \left ( \sqrt {3} \sqrt [3]{-{x}^{-6}}{x}^{3}+3\,\tan \left ( {\it RootOf} \left ( -18\,{x }^{3} \left ( -{x}^{-6} \right ) ^{2/3}-6\,{\it \_Z}\,\sqrt {3}-\ln \left ( {\frac { \left ( \sqrt {3}+\tan \left ( {\it \_Z} \right ) \right ) ^{6}}{ \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) ^{3}}} \right ) +18\,{\it \_C1} \right ) \right ) {x}^{3} \sqrt [3]{-{x}^{-6}}-2\,\sqrt {3} \right ) } \right \} \]