\[ \boxed { {x}^{3} \left ( y \left ( x \right ) \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( y \left ( x \right ) +x \right ) \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) \right ) ^{3}=0} \]
Mathematica: cpu = 38.092837 (sec), leaf count = 37 \[ \text {DSolve}\left [x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0,y(x),x\right ] \]
Maple: cpu = 1.716 (sec), leaf count = 166 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -2\,\ln \left ( x \right ) -\int ^{{\it \_Z}}\!{1 \left ( i\sqrt {3}{{\sl Y}_{i\sqrt {3} }\left (2\,\sqrt {{\it \_f}}\right )}{\it \_C1}\,\sqrt {{\it \_f}}+i \sqrt {3}{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}\sqrt {{\it \_f}}+{{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}{ \it \_C1}\,\sqrt {{\it \_f}}-2\,{\it \_C1}\,{{\sl Y}_{i\sqrt {3}+1 }\left (2\,\sqrt {{\it \_f}}\right )}{\it \_f}+{{\sl J}_{i\sqrt {3} }\left (2\,\sqrt {{\it \_f}}\right )}\sqrt {{\it \_f}}-2\,{{\sl J}_{i \sqrt {3}+1}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_f} \right ) {{\it \_f}}^{-{\frac {3}{2}}} \left ( {{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{ \it \_f}}\right )}{\it \_C1}+{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )} \right ) ^{-1}}{d{\it \_f}}+2\,{\it \_C2} \right ) x \right \} \]