#### 2.722   ODE No. 722

$y'(x)=-\frac {y(x)^3}{x (-y(x)+2 y(x) \log (x)-1)}$ Mathematica : cpu = 20.5491 (sec), leaf count = 490

$\text {Solve}\left [-\frac {\sqrt [3]{-2} \left ((-2)^{2/3}-\frac {(1-2 \log (x))^2 \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (y(x) (5-4 \log (x))+2)}{2 \sqrt [3]{2} (y(x) (2 \log (x)-1)-1)}\right ) \left (\frac {y(x) (4 \log (x)-5)-2}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(2 \log (x)-1)^3}} (2 \log (x)-1) (y(x) (2 \log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\log \left (\frac {y(x) (5-4 \log (x))+2}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(2 \log (x)-1)^3}} (2 \log (x)-1) (y(x) (2 \log (x)-1)-1)}+2 (-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2 (y(x) (4 \log (x)-5)-2)}{y(x) (4 \log (x)-2)-2}+1\right )-\log \left (\frac {y(x) (4 \log (x)-5)-2}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(2 \log (x)-1)^3}} (2 \log (x)-1) (y(x) (2 \log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2 (y(x) (4 \log (x)-5)-2)}{y(x) (4 \log (x)-2)-2}+1\right )+3\right )}{9 \left (\frac {(y(x) (4 \log (x)-5)-2)^3}{8 (y(x) (2 \log (x)-1)-1)^3}+\frac {3 \sqrt [3]{-1} (y(x) (4 \log (x)-5)-2)}{2 (1-2 \log (x))^4 \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{4/3} (y(x) (2 \log (x)-1)-1)}+2\right )}=\frac {4}{9} 2^{2/3} \log (x) \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2+c_1,y(x)\right ]$ Maple : cpu = 1.11 (sec), leaf count = 70

$\left \{ y \left ( x \right ) ={{{\rm e}^{{\it RootOf} \left ( -{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}+2}{2\,{x}^{4}}} \right ) +3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+2 \right ) }} \left ( 1+ \left ( 2\,\ln \left ( x \right ) -1 \right ) {{\rm e}^{{\it RootOf} \left ( -{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}+2}{2\,{x}^{4}}} \right ) +3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+2 \right ) }} \right ) ^{-1}} \right \}$