\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( {x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+y \left ( x \right ) x{{\rm e}^{x}}+ \left ( {{\rm e}^{x}} \right ) ^{2} \right ) \left ( x-1 \right ) }{x \left ( {{\rm e}^{x}} \right ) ^{2}}}=0} \]
Mathematica: cpu = 3.039386 (sec), leaf count = 426 \[ \text {Solve}\left [-\frac {\sqrt [3]{2} \left (\frac {3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)}{\sqrt [3]{2} \sqrt [3]{e^{-3 x} (x-1)^3}}+2^{2/3}\right ) \left (2^{2/3}-\frac {2^{2/3} \left (3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)\right )}{\sqrt [3]{e^{-3 x} (x-1)^3}}\right ) \left (\left (1-\frac {3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)}{\sqrt [3]{e^{-3 x} (x-1)^3}}\right ) \log \left (\frac {3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)}{\sqrt [3]{2} \sqrt [3]{e^{-3 x} (x-1)^3}}+2^{2/3}\right )+\left (\frac {3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)}{\sqrt [3]{e^{-3 x} (x-1)^3}}-1\right ) \log \left (2^{2/3}-\frac {2^{2/3} \left (3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)\right )}{\sqrt [3]{e^{-3 x} (x-1)^3}}\right )+3\right )}{9 \left (-\frac {e^{3 x} \left (3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)\right )^3}{(x-1)^3}+\frac {3 \left (3 e^{-2 x} x (x-1) y(x)+e^{-x} (x-1)\right )}{\sqrt [3]{e^{-3 x} (x-1)^3}}-2\right )}=c_1+\frac {2^{2/3} e^{-x} (x-1) (x-\log (x))}{9 \sqrt [3]{e^{-3 x} (x-1)^3}},y(x)\right ] \]
Maple: cpu = 0.203 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={\frac {1}{9\,x}{{\rm e}^{{\it RootOf} \left ( -{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac {x \left ( {{\rm e}^{{ \it \_Z}}}+9 \right ) }{2}} \right ) +3\,{\it \_C1}\,{{\rm e}^{{\it \_Z} }}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+x{{\rm e}^{{\it \_Z}}}+9 \right ) + x}}} \right \} \]