\[ x^3 y(x)^2 y''(x)+(y(x)+x) \left (x y'(x)-y(x)\right )^3=0 \] ✗ Mathematica : cpu = 40.7807 (sec), leaf count = 0 , could not solve
DSolve[(x + y[x])*(-y[x] + x*Derivative[1][y][x])^3 + x^3*y[x]^2*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 0.274 (sec), leaf count = 166
\[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -2\,\ln \left ( x \right ) -\int ^{{\it \_Z}}\!{1 \left ( i\sqrt {3}{{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_C1}\,\sqrt {{\it \_f}}+i\sqrt {3}{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}\sqrt {{\it \_f}}+{{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_C1}\,\sqrt {{\it \_f}}-2\,{\it \_C1}\,{{\sl Y}_{i\sqrt {3}+1}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_f}+{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}\sqrt {{\it \_f}}-2\,{{\sl J}_{i\sqrt {3}+1}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_f} \right ) {{\it \_f}}^{-{\frac {3}{2}}} \left ( {{\sl Y}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )}{\it \_C1}+{{\sl J}_{i\sqrt {3}}\left (2\,\sqrt {{\it \_f}}\right )} \right ) ^{-1}}{d{\it \_f}}+2\,{\it \_C2} \right ) x \right \} \]