\[ y'(x)=\frac {x^3 \sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.515458 (sec), leaf count = 105
\[\left \{\left \{y(x)\to \frac {1}{72} \left (16 x^6-48 x^5+132 x^4-144 x^3+135 x^2-96 x^3 \log (x+1)+144 x^2 \log (x+1)-96 c_1 x^3+144 c_1 x^2+18 x+144 \log ^2(x+1)-288 x \log (x+1)-288 c_1 x+288 c_1 \log (x+1)-9+144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.657 (sec), leaf count = 40
\[ \left \{ {\it \_C1}+{\frac {4\,{x}^{3}}{3}}-2\,{x}^{2}+4\,x-4\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]