\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {x+1+2\,\sqrt {4\,{x}^{2}y \left ( x \right ) +1}{x}^{3}}{{x}^{3} \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.299538 (sec), leaf count = 66 \[ \left \{\left \{y(x)\to \frac {-8 c_1 x^3+4 c_1^2 x^2+8 c_1 x^2 \log (x+1)+4 x^4-8 x^3 \log (x+1)+4 x^2 \log ^2(x+1)-1}{4 x^2}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 30 \[ \left \{ -2\,\ln \left ( 1+x \right ) +2\,x-{\frac {1}{x}\sqrt {4\,{x}^ {2}y \left ( x \right ) +1}}+{\it \_C1}=0 \right \} \]