#### 2.683   ODE No. 683

$y'(x)=\frac {y(x) \left (x^4 y(x) \log (x (x+1))-x^3 \log (x (x+1))-1\right )}{x}$ Mathematica : cpu = 1.0741 (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 = 0.368 (sec), leaf count = 114

$\left \{ y \left ( x \right ) ={ \left ( \left ( x \left ( 1+x \right ) \right ) ^{{\frac {{x}^{3}}{3}}} \right ) ^{-1} \left ( \sqrt [3]{1+x}{{\rm e}^{-{\frac {2\,{x}^{3}}{9}}+{\frac {{x}^{2}}{6}}-{\frac {x}{3}}}}{\it \_C1}\,x+{x}^{1-{\frac {{x}^{3}}{3}}} \left ( 1+x \right ) ^{-{\frac {{x}^{3}}{3}}}{{\rm e}^{{\frac {i}{6}}{x}^{3} \left ( {\it csgn} \left ( i+ix \right ) -{\it csgn} \left ( ix \left ( 1+x \right ) \right ) \right ) \left ( -{\it csgn} \left ( ix \left ( 1+x \right ) \right ) +{\it csgn} \left ( ix \right ) \right ) {\it csgn} \left ( ix \left ( 1+x \right ) \right ) \pi }} \right ) ^{-1}} \right \}$