\[ y'(x)=\frac {-\frac {x^2}{4}+x^3 \sqrt {x^2+8 y(x)-2 x+1}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.508206 (sec), leaf count = 105
\[\left \{\left \{y(x)\to \frac {1}{72} \left (16 x^6-48 x^5+132 x^4-144 x^3-96 x^3 \log (x+1)-96 c_1 x^3+135 x^2+144 x^2 \log (x+1)+144 c_1 x^2+18 x+144 \log ^2(x+1)-288 x \log (x+1)-288 c_1 x+288 c_1 \log (x+1)-9+144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.533 (sec), leaf count = 40
\[c_{1}+\frac {4 x^{3}}{3}-2 x^{2}+4 x -4 \ln \left (1+x \right )-\sqrt {x^{2}-2 x +1+8 y \relax (x )} = 0\]