\[ (x+1) y'(x)+y(x) (y(x)-x)=0 \] ✓ Mathematica : cpu = 0.192605 (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 = 0.044 (sec), leaf count = 33
\[y \relax (x ) = \frac {{\mathrm e}^{x}}{-{\mathrm e}^{-1} \left (1+x \right ) \Ei \left (1, -1-x \right )-{\mathrm e}^{x}+c_{1} \left (1+x \right )}\]