\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/2\,{\frac {{x}^{2}-x-2-2\,\sqrt {{x}^{2}-4\,x+4\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.233530 (sec), leaf count = 40 \[ \left \{\left \{y(x)\to \frac {1}{4} \left (-8 c_1 \log (x+1)+4 c_1^2-x^2+4 x+4 \log ^2(x+1)\right )\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 27 \[ \left \{ {\it \_C1}+2\,\ln \left ( 1+x \right ) -1-\sqrt {{x}^{2}-4\,x+ 4\,y \left ( x \right ) }=0 \right \} \]