\[ y'(x)=\frac {y(x) \left (x^3 y(x)+x^2 y(x) \log (x)-x^2-x-x \log (x)+1\right )}{(x-1) x} \] ✓ Mathematica : cpu = 0.609317 (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 = 0.234 (sec), leaf count = 44
\[\left \{y \left (x \right ) = \frac {{\mathrm e}^{-x} {\mathrm e}^{\dilog \left (x \right )}}{\left (c_{1}+\int -\frac {\left (x +\ln \left (x \right )\right ) {\mathrm e}^{-x} {\mathrm e}^{\dilog \left (x \right )}}{\left (x -1\right )^{2}}d x \right ) \left (x -1\right ) x}\right \}\]