\[ y'(x)=\frac {x^6 \sqrt {4 x^2 y(x)+1}+\frac {x}{2}+\frac {1}{2}}{x^3 (x+1)} \] ✓ Mathematica : cpu = 0.433268 (sec), leaf count = 144
\[\left \{\left \{y(x)\to \frac {9 x^{10}-24 x^9+52 x^8-120 x^7+132 x^6-144 x^5+144 x^4+144 x^2 \log ^2(x+1)+72 x^6 \log (x+1)-96 x^5 \log (x+1)+144 x^4 \log (x+1)-288 x^3 \log (x+1)-72 c_1 x^6+96 c_1 x^5-144 c_1 x^4+288 c_1 x^3+144 c_1{}^2 x^2-288 c_1 x^2 \log (x+1)-36}{144 x^2}\right \}\right \}\] ✓ Maple : cpu = 0.763 (sec), leaf count = 43
\[ \left \{ {\it \_C1}+2\,\ln \left ( 1+x \right ) -{\frac {1}{x}\sqrt {4\,{x}^{2}y \left ( x \right ) +1}}-2\,x+{x}^{2}-{\frac {2\,{x}^{3}}{3}}+{\frac {{x}^{4}}{2}}=0 \right \} \]