\[ y'(x)=\frac {\sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.236188 (sec), leaf count = 45
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-32 c_1 \log (4 (x+1))+16 c_1^2-x^2+2 x+16 \log ^2(4 (x+1))-1\right )\right \}\right \}\] ✓ Maple : cpu = 0.314 (sec), leaf count = 28
\[ \left \{ {\it \_C1}+4\,\ln \left ( 1+x \right ) -{\frac {1}{4}}-\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]