\[ y'(x)=\frac {y(x) \left (x^3 y(x)+x^2 y(x) \log (x)-x^2-x-x \log (x)+1\right )}{(x-1) x} \] ✓ Mathematica : cpu = 0.455162 (sec), leaf count = 101
DSolve[Derivative[1][y][x] == (y[x]*(1 - x - x^2 - x*Log[x] + x^3*y[x] + x^2*Log[x]*y[x]))/((-1 + x)*x),y[x],x]
\[\left \{\left \{y(x)\to -\frac {e^{-\text {Li}_2(x)-x} (1-x)^{-\log (x)}}{(x-1) x \left (-\int _1^x\frac {\exp (-K[1]-\log (1-K[1]) (\log (K[1])+1)-\text {Li}_2(K[1])) \left (K[1]^3+\log (K[1]) K[1]^2\right )}{(K[1]-1) K[1]^2}dK[1]+c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.23 (sec), leaf count = 44
dsolve(diff(y(x),x) = y(x)*(1-x+y(x)*x^2*ln(x)+x^3*y(x)-x*ln(x)-x^2)/(x-1)/x,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\dilog \left (x \right )} {\mathrm e}^{-x}}{x \left (\int -\frac {{\mathrm e}^{\dilog \left (x \right )} \left (x +\ln \left (x \right )\right ) {\mathrm e}^{-x}}{\left (x -1\right )^{2}}d x +c_{1}\right ) \left (x -1\right )}\]