\[ (x+1) y'(x)+y(x) (y(x)-x)=0 \] ✓ Mathematica : cpu = 0.149502 (sec), leaf count = 44
DSolve[y[x]*(-x + y[x]) + (1 + x)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {e^{x+1}}{-x \operatorname {ExpIntegralEi}(x+1)-\operatorname {ExpIntegralEi}(x+1)+e^{x+1}-e c_1 x-e c_1}\right \}\right \}\] ✓ Maple : cpu = 0.031 (sec), leaf count = 33
dsolve((1+x)*diff(y(x),x)+y(x)*(y(x)-x) = 0,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{x}}{-{\mathrm e}^{-1} \left (1+x \right ) \operatorname {expIntegral}_{1}\left (-1-x \right )-{\mathrm e}^{x}+c_{1} \left (1+x \right )}\]