\[ y'(x)=\frac {x^6 \sqrt {4 x^2 y(x)+1}+\frac {x}{2}+\frac {1}{2}}{x^3 (x+1)} \] ✓ Mathematica : cpu = 0.286888 (sec), leaf count = 120
\[\left \{\left \{y(x)\to -\frac {1}{12} \left (6 c_1-11\right ) x^4+\left (\frac {2 c_1}{3}-1\right ) x^3-\left (c_1-1\right ) x^2+\left (-2 c_1+\frac {x^4}{2}-\frac {2 x^3}{3}+x^2-2 x\right ) \log (x+1)+2 c_1 x+c_1^2+\frac {x^8}{16}-\frac {x^7}{6}+\frac {13 x^6}{36}-\frac {5 x^5}{6}-\frac {1}{4 x^2}+\log ^2(x+1)\right \}\right \}\]
✓ Maple : cpu = 0.626 (sec), leaf count = 43
\[ \left \{ {\it \_C1}+2\,\ln \left ( 1+x \right ) -{\frac {1}{x}\sqrt {4\,{x}^{2}y \left ( x \right ) +1}}-2\,x+{x}^{2}-{\frac {2\,{x}^{3}}{3}}+{\frac {{x}^{4}}{2}}=0 \right \} \]