#### 2.844   ODE No. 844

$y'(x)=\frac {y(x) (y(x)+1) (y(x)+x)}{x (x y(x)+y(x)+x)}$ Mathematica : cpu = 13.0211 (sec), leaf count = 386

$\text {Solve}\left [\frac {2^{2/3} \left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right ) \left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}+2\right ) \left (\left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right ) \log \left (2^{2/3} \left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right )\right )+\left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}-1\right ) \log \left (2^{2/3} \left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}+2\right )\right )-3\right )}{9 \left (\frac {3 \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}-\frac {((x-2) y(x)+x)^3}{((x+1) y(x)+x)^3}-2\right )}=c_1+\frac {2^{2/3} \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2}{9 x^3},y(x)\right ]$ Maple : cpu = 0.148 (sec), leaf count = 97

$\left \{ y \left ( x \right ) =-{x{{\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{\it \_Z}}}+3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+{{\rm e}^{{\it \_Z}}}x+9 \right ) }} \left ( {{\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{\it \_Z}}}+3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+{{\rm e}^{{\it \_Z}}}x+9 \right ) }}x+{{\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{\it \_Z}}}+3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+{{\rm e}^{{\it \_Z}}}x+9 \right ) }}+9 \right ) ^{-1}} \right \}$