\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {{x}^{2}+2\,x+1+2\,\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.235530 (sec), leaf count = 39 \[ \left \{\left \{y(x)\to \frac {1}{4} \left (8 c_1 \log (x+1)-4 c_1^2+x^2+2 x-4 \log ^2(x+1)+1\right )\right \}\right \} \]
Maple: cpu = 0.218 (sec), leaf count = 28 \[ \left \{ {\it \_C1}-2\,\ln \left ( 1+x \right ) -{\frac {1}{2}}-\sqrt { {x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0 \right \} \]