#### 2.724   ODE No. 724

$y'(x)=-\frac {y(x)^3}{x (-y(x)+y(x) \log (x)-1)}$ Mathematica : cpu = 13.9802 (sec), leaf count = 422

$\text {Solve}\left [-\frac {\sqrt [3]{-2} \left (\frac {1-y(x) (\log (x)-4)}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {2^{2/3} (y(x) (\log (x)-4)-1)}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\log \left (\frac {2^{2/3} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+2 (-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+1\right )-\log \left (\frac {2^{2/3} (y(x) (\log (x)-4)-1)}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+1\right )+3\right )}{9 \left (\frac {(y(x) (\log (x)-4)-1)^3}{(y(x) (\log (x)-1)-1)^3}+\frac {3 \sqrt [3]{-1} (y(x) (\log (x)-4)-1)}{\left (-\frac {1}{(\log (x)-1)^3}\right )^{4/3} (\log (x)-1)^4 (y(x) (\log (x)-1)-1)}+2\right )}=\frac {1}{9} 2^{2/3} \left (-\frac {1}{(\log (x)-1)^3}\right )^{2/3} \log (x) (\log (x)-1)^2+c_1,y(x)\right ]$ Maple : cpu = 0.092 (sec), leaf count = 18

$\left \{ y \left ( x \right ) = \left ( -{\it lambertW} \left ( {\it \_C1}\,{{\rm e}^{-2}}x \right ) +\ln \left ( x \right ) -2 \right ) ^{-1} \right \}$