\[ y'(x)=\frac {y(x) \left (x^4 y(x) \log (x (x+1))-x^3 \log (x (x+1))-1\right )}{x} \] ✓ Mathematica : cpu = 0.717697 (sec), leaf count = 84
DSolve[Derivative[1][y][x] == (y[x]*(-1 - x^3*Log[x*(1 + x)] + x^4*Log[x*(1 + x)]*y[x]))/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {e^{\frac {2 x^3}{9}+\frac {x}{3}}}{e^{\frac {x^2}{6}+\frac {1}{18} \left (4 x^2-3 x+6\right ) x} x+c_1 e^{\frac {x^2}{6}} x \sqrt [3]{x+1} (x (x+1))^{\frac {x^3}{3}}}\right \}\right \}\] ✓ Maple : cpu = 0.07 (sec), leaf count = 45
dsolve(diff(y(x),x) = y(x)*(-1+ln(x*(1+x))*y(x)*x^4-ln(x*(1+x))*x^3)/x,y(x))
\[y \left (x \right ) = \frac {1}{x \left (\left (x \left (1+x \right )\right )^{\frac {x^{3}}{3}} c_{1} \left (1+x \right )^{\frac {1}{3}} {\mathrm e}^{-\frac {2}{9} x^{3}+\frac {1}{6} x^{2}-\frac {1}{3} x}+1\right )}\]