\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac { \left ( y \left ( x \right ) \right ) ^{3}}{ \left ( -1+y \left ( x \right ) \ln \left ( x \right ) -y \left ( x \right ) \right ) x}}=0} \]
Mathematica: cpu = 64.507191 (sec), leaf count = 420 \[ \text {Solve}\left [\frac {\sqrt [3]{-2} \left (\frac {1-y(x) (\log (x)-4)}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {2^{2/3} (y(x) (\log (x)-4)-1)}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (-\log \left (\frac {1-y(x) (\log (x)-4)}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+1\right )+\log \left (\frac {2^{2/3} (y(x) (\log (x)-4)-1)}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} (1-y(x) (\log (x)-4))}{\sqrt [3]{-\frac {1}{(\log (x)-1)^3}} (\log (x)-1) (y(x) (\log (x)-1)-1)}+1\right )-3\right )}{9 \left (\frac {(y(x) (\log (x)-4)-1)^3}{(y(x) (\log (x)-1)-1)^3}+\frac {3 \sqrt [3]{-1} (y(x) (\log (x)-4)-1)}{\left (-\frac {1}{(\log (x)-1)^3}\right )^{4/3} (\log (x)-1)^4 (y(x) (\log (x)-1)-1)}+2\right )}=c_1+\frac {1}{9} 2^{2/3} \left (-\frac {1}{(\log (x)-1)^3}\right )^{2/3} \log (x) (\log (x)-1)^2,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 18 \[ \left \{ y \left ( x \right ) = \left ( -{\it lambertW} \left ( {\it \_C1} \,{{\rm e}^{-2}}x \right ) +\ln \left ( x \right ) -2 \right ) ^{-1} \right \} \]