\[ y'(x)=\frac {y(x) \left (x^3 y(x)+x^2 y(x) \log (x)-x^2-x-x \log (x)+1\right )}{(x-1) x} \] ✓ Mathematica : cpu = 0.439658 (sec), leaf count = 101
\[\left \{\left \{y(x)\to -\frac {e^{-\text {Li}_2(x)-x} (1-x)^{-\log (x)}}{(x-1) x \left (-\int _1^x\frac {\exp (-K[1]-\log (1-K[1]) (\log (K[1])+1)-\text {Li}_2(K[1])) \left (K[1]^3+\log (K[1]) K[1]^2\right )}{(K[1]-1) K[1]^2}dK[1]+c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.612 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it dilog} \left ( x \right ) }}}{x{{\rm e}^{x}} \left ( x-1 \right ) } \left ( \int \!-{\frac {{{\rm e}^{{\it dilog} \left ( x \right ) }} \left ( x+\ln \left ( x \right ) \right ) }{{{\rm e}^{x}} \left ( x-1 \right ) ^{2}}}\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]