\[ y'(x)=\frac {\sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.256699 (sec), leaf count = 46
\[\left \{\left \{y(x)\to \frac {1}{8} \left (16 c_1^2-x^2+2 x-1\right )-4 c_1 \log (4 (x+1))+2 \log ^2(4 (x+1))\right \}\right \}\]
✓ Maple : cpu = 0.306 (sec), leaf count = 28
\[ \left \{ {\it \_C1}+4\,\ln \left ( 1+x \right ) -{\frac {1}{4}}-\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]