\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {xy \left ( x \right ) -y \left ( x \right ) -{{\rm e}^{1+x}}{x}^{3}+{{\rm e}^{1+x}}x \left ( y \left ( x \right ) \right ) ^{2}}{x \left ( x-1 \right ) }}=0} \]
Mathematica: cpu = 0.075010 (sec), leaf count = 60 \[ \left \{\left \{y(x)\to -\frac {x \left (e^{2 c_1+2 e^2 \text {Ei}(x-1)+2 e^{x+1}}-1\right )}{e^{2 c_1+2 e^2 \text {Ei}(x-1)+2 e^{x+1}}+1}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) =-\tanh \left ( {{\rm e}^{1+x}}-{{\rm e}^{2 }}{\it Ei} \left ( 1,1-x \right ) +{\it \_C1} \right ) x \right \} \]