\[ y'(x)=\frac {\sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.417135 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-x^2+2 x+16 \log ^2(x+1)-32 c_1 \log (x+1)-1+16 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.462 (sec), leaf count = 28
\[c_{1}+4 \ln \left (1+x \right )-\frac {1}{4}-\sqrt {x^{2}-2 x +1+8 y \relax (x )} = 0\]