\[ y'(x)=\frac {-\frac {x^2}{4}+x^3 \sqrt {x^2+8 y(x)-2 x+1}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.281456 (sec), leaf count = 106
\[\left \{\left \{y(x)\to -\frac {2}{3} \left (-6 c_1+2 x^3-3 x^2+6 x+11\right ) \log (4 (x+1))+\frac {1}{72} \left (\left (32-96 c_1\right ) x^3+3 \left (48 c_1-43\right ) x^2-6 \left (48 c_1-91\right ) x+144 c_1^2-528 c_1+16 x^6-48 x^5+132 x^4+475\right )+2 \log ^2(4 (x+1))\right \}\right \}\]
✓ Maple : cpu = 0.346 (sec), leaf count = 40
\[ \left \{ {\it \_C1}+{\frac {4\,{x}^{3}}{3}}-2\,{x}^{2}+4\,x-4\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]