\[ y'(x)=\frac {\sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.53068 (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 = 0.422 (sec), leaf count = 28
\[\left \{c_{1}+4 \ln \left (x +1\right )-\frac {1}{4}-\sqrt {x^{2}-2 x +8 y \left (x \right )+1} = 0\right \}\]