\[ (x-y(x)) y''(x)+2 y'(x) \left (y'(x)+1\right )=0 \] ✓ Mathematica : cpu = 0.25525 (sec), leaf count = 38
\[\left \{\left \{y(x)\to -\frac {e^{-c_1} \left (e^{c_1} c_2 x+e^{c_1} c_2^2+1\right )}{c_2+x}\right \}\right \}\] ✓ Maple : cpu = 0.696 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\frac {{{\it \_C2}}^{2}-{\it \_C2}\,x+{\it \_C1}}{{\it \_C2}-x}} \right \} \]