\[ y'(x)=\frac {\sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.408618 (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 = 0.616 (sec), leaf count = 28
\[ \left \{ {\it \_C1}+4\,\ln \left ( 1+x \right ) -{\frac {1}{4}}-\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]