\[ y'(x)=\frac {x^3 \sqrt {4 x^2 y(x)+1}+\frac {x}{2}+\frac {1}{2}}{x^3 (x+1)} \] ✓ Mathematica : cpu = 0.265644 (sec), leaf count = 43
\[\left \{\left \{y(x)\to -2 c_1 x-2 \left (x-c_1\right ) \log (x+1)+c_1^2+x^2-\frac {1}{4 x^2}+\log ^2(x+1)\right \}\right \}\]
✓ Maple : cpu = 0.279 (sec), leaf count = 30
\[ \left \{ -2\,\ln \left ( 1+x \right ) -{\frac {1}{x}\sqrt {4\,{x}^{2}y \left ( x \right ) +1}}+2\,x+{\it \_C1}=0 \right \} \]