\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {{x}^{2}+2\,x+1+2\,{x}^{3}\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.296038 (sec), leaf count = 115 \[ \left \{\left \{y(x)\to \frac {1}{36} \left (24 c_1 x^3-36 c_1 x^2+72 c_1 x-72 c_1 \log (x+1)-36 c_1^2+132 c_1-4 x^6+12 x^5-33 x^4-8 x^3+24 x^3 \log (x+1)+39 x^2-36 x^2 \log (x+1)-114 x-36 \log ^2(x+1)+72 x \log (x+1)+132 \log (x+1)-112\right )\right \}\right \} \]
Maple: cpu = 0.265 (sec), leaf count = 38 \[ \left \{ {\it \_C1}-{\frac {2\,{x}^{3}}{3}}+{x}^{2}-2\,x+2\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0 \right \} \]