\[ (x+1) y'(x)+y(x) (y(x)-x)=0 \] ✓ Mathematica : cpu = 0.0282808 (sec), leaf count = 44
\[\left \{\left \{y(x)\to -\frac {e^{x+1}}{-e c_1 x-e c_1-x \text {Ei}(x+1)-\text {Ei}(x+1)+e^{x+1}}\right \}\right \}\]
✓ Maple : cpu = 0.031 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) =-{\frac {{{\rm e}^{x}}}{{{\rm e}^{-1}}{\it Ei} \left ( 1,-1-x \right ) x+{{\rm e}^{-1}}{\it Ei} \left ( 1,-1-x \right ) -{\it \_C1}\,x+{{\rm e}^{x}}-{\it \_C1}}} \right \} \]