\[ y'(x)=\frac {y(x) \left (x^4 y(x) \log (x (x+1))-x^3 \log (x (x+1))-1\right )}{x} \] ✓ Mathematica : cpu = 1.01087 (sec), leaf count = 84
\[\left \{\left \{y(x)\to \frac {e^{\frac {2 x^3}{9}+\frac {x}{3}}}{e^{\frac {x^2}{6}+\frac {1}{18} \left (4 x^2-3 x+6\right ) x} x+c_1 e^{\frac {x^2}{6}} x \sqrt [3]{x+1} (x (x+1))^{\frac {x^3}{3}}}\right \}\right \}\] ✓ Maple : cpu = 0.162 (sec), leaf count = 114
\[y \relax (x ) = \frac {\left (x \left (1+x \right )\right )^{-\frac {x^{3}}{3}}}{\left (1+x \right )^{\frac {1}{3}} {\mathrm e}^{-\frac {2}{9} x^{3}+\frac {1}{6} x^{2}-\frac {1}{3} x} c_{1} x +x^{1-\frac {x^{3}}{3}} \left (1+x \right )^{-\frac {x^{3}}{3}} {\mathrm e}^{\frac {i x^{3} \mathrm {csgn}\left (i x \left (1+x \right )\right ) \pi \left (-\mathrm {csgn}\left (i x \left (1+x \right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (\mathrm {csgn}\left (i x +i\right )-\mathrm {csgn}\left (i x \left (1+x \right )\right )\right )}{6}}}\]