\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac { \left ( y \left ( x \right ) \right ) ^{3}}{ \left ( -1+2\,y \left ( x \right ) \ln \left ( x \right ) -y \left ( x \right ) \right ) x}}=0} \]
Mathematica: cpu = 63.894114 (sec), leaf count = 491 \[ \text {Solve}\left [\frac {\sqrt [3]{-2} \left ((-2)^{2/3}-\frac {(1-2 \log (x))^2 \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (y(x) (5-4 \log (x))+2)}{2 \sqrt [3]{2} (y(x) (2 \log (x)-1)-1)}\right ) \left (\frac {y(x) (4 \log (x)-5)-2}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(2 \log (x)-1)^3}} (2 \log (x)-1) (y(x) (2 \log (x)-1)-1)}+(-2)^{2/3}\right ) \left (-\log \left ((-2)^{2/3}-\frac {(1-2 \log (x))^2 \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (y(x) (5-4 \log (x))+2)}{2 \sqrt [3]{2} (y(x) (2 \log (x)-1)-1)}\right ) \left (\frac {\sqrt [3]{-1} \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2 (y(x) (4 \log (x)-5)-2)}{y(x) (4 \log (x)-2)-2}+1\right )+\log \left (\frac {y(x) (4 \log (x)-5)-2}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(2 \log (x)-1)^3}} (2 \log (x)-1) (y(x) (2 \log (x)-1)-1)}+(-2)^{2/3}\right ) \left (\frac {\sqrt [3]{-1} \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2 (y(x) (4 \log (x)-5)-2)}{y(x) (4 \log (x)-2)-2}+1\right )-3\right )}{9 \left (\frac {(y(x) (4 \log (x)-5)-2)^3}{8 (y(x) (2 \log (x)-1)-1)^3}+\frac {3 \sqrt [3]{-1} (y(x) (4 \log (x)-5)-2)}{2 (1-2 \log (x))^4 \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{4/3} (y(x) (2 \log (x)-1)-1)}+2\right )}=c_1+\frac {4}{9} 2^{2/3} \log (x) \left (-\frac {1}{(2 \log (x)-1)^3}\right )^{2/3} (1-2 \log (x))^2,y(x)\right ] \]
Maple: cpu = 0.281 (sec), leaf count = 96 \[ \left \{ y \left ( x \right ) ={1{{\rm e}^{{\it RootOf} \left ( -{{\rm e} ^{{\it \_Z}}}\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}+2}{2\,{x}^{4}}} \right ) +3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{ \it \_Z}}}+2 \right ) }} \left ( 2\,{{\rm e}^{{\it RootOf} \left ( -{ {\rm e}^{{\it \_Z}}}\ln \left ( 1/2\,{\frac {{{\rm e}^{{\it \_Z}}}+2}{ {x}^{4}}} \right ) +3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{ {\rm e}^{{\it \_Z}}}+2 \right ) }}\ln \left ( x \right ) -{{\rm e}^{{ \it RootOf} \left ( -{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac {{{\rm e}^ {{\it \_Z}}}+2}{2\,{x}^{4}}} \right ) +3\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+2 \right ) }}+1 \right ) ^{-1}} \right \} \]