\[ (x+1) y'(x)+y(x) (y(x)-x)=0 \] ✓ Mathematica : cpu = 0.164196 (sec), leaf count = 44
\[\left \{\left \{y(x)\to -\frac {e^{x+1}}{-x \text {Ei}(x+1)-\text {Ei}(x+1)+e^{x+1}-e c_1 x-e c_1}\right \}\right \}\] ✓ Maple : cpu = 0.027 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{x}}}{-{{\rm e}^{-1}} \left ( 1+x \right ) {\it Ei} \left ( 1,-1-x \right ) -{{\rm e}^{x}}+{\it \_C1}\, \left ( 1+x \right ) }} \right \} \]