#### 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 = 1.10817 (sec), leaf count = 84

$\left \{\left \{y(x)\to \frac {e^{\frac {2 x^3}{9}+\frac {x}{3}}}{c_1 e^{\frac {x^2}{6}} x \sqrt [3]{x+1} (x (x+1))^{\frac {x^3}{3}}+e^{\frac {x^2}{6}+\frac {1}{18} \left (4 x^2-3 x+6\right ) x} x}\right \}\right \}$ Maple : cpu = 0.082 (sec), leaf count = 152

$\left \{ y \left ( x \right ) ={\frac {1}{x} \left ( x \left ( 1+x \right ) \right ) ^{-{\frac {{x}^{3}}{3}}}{{\rm e}^{{\frac {2\,{x}^{3}}{9}}}}{{\rm e}^{-{\frac {{x}^{2}}{6}}}}{{\rm e}^{{\frac {x}{3}}}} \left ( \left ( 1+x \right ) ^{-{\frac {{x}^{3}}{3}}}{x}^{-{\frac {{x}^{3}}{3}}}{{\rm e}^{{\frac {x}{6} \left ( i{x}^{2}\pi \, \left ( {\it csgn} \left ( ix \left ( 1+x \right ) \right ) \right ) ^{3}-i \left ( {\it csgn} \left ( ix \right ) +{\it csgn} \left ( i+ix \right ) \right ) {x}^{2}\pi \, \left ( {\it csgn} \left ( ix \left ( 1+x \right ) \right ) \right ) ^{2}+i{x}^{2}\pi \,{\it csgn} \left ( ix \left ( 1+x \right ) \right ) {\it csgn} \left ( ix \right ) {\it csgn} \left ( i+ix \right ) +{\frac {4\,{x}^{2}}{3}}-x+2 \right ) }}}+{\it \_C1}\,\sqrt [3]{1+x} \right ) ^{-1}} \right \}$