\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/4\,{\frac {{x}^{2}-1-4\,\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.247531 (sec), leaf count = 45 \[ \left \{\left \{y(x)\to \frac {1}{8} \left (-32 c_1 \log (4 (x+1))+16 c_1^2-x^2+2 x+16 \log ^2(4 (x+1))-1\right )\right \}\right \} \]
Maple: cpu = 0.218 (sec), leaf count = 28 \[ \left \{ {\it \_C1}+4\,\ln \left ( 1+x \right ) -{\frac {1}{4}}-\sqrt { {x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]