\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \ln \left ( x-1 \right ) +{x}^{4}+{x}^{3}+{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+x \left ( y \left ( x \right ) \right ) ^{2}}{\ln \left ( x-1 \right ) x}}=0} \]
Mathematica: cpu = 0.052007 (sec), leaf count = 34 \[ \left \{\left \{y(x)\to x \tan \left (c_1+2 \text {Ei}(\log (x-1))+3 \text {Ei}(2 \log (x-1))+\text {Ei}(3 \log (x-1))\right )\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =\tan \left ( -{\it Ei} \left ( 1,-3\,\ln \left ( x-1 \right ) \right ) -3\,{\it Ei} \left ( 1,-2\,\ln \left ( x-1 \right ) \right ) -2\,{\it Ei} \left ( 1,-\ln \left ( x-1 \right ) \right ) +{\it \_C1} \right ) x \right \} \]