\[ y'(x)=\frac {-\frac {x^2}{4}+x^3 \sqrt {x^2+8 y(x)-2 x+1}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.319304 (sec), leaf count = 127
\[\left \{\left \{y(x)\to \frac {1}{72} \left (-96 c_1 x^3+144 c_1 x^2-288 c_1 x+288 c_1 \log (4 x+4)+144 c_1^2-528 c_1+16 x^6-48 x^5+132 x^4+32 x^3-96 x^3 \log (4 x+4)-129 x^2+144 x^2 \log (4 x+4)+546 x+144 \log ^2(4 x+4)-288 x \log (4 x+4)-528 \log (4 x+4)+475\right )\right \}\right \}\] ✓ Maple : cpu = 0.37 (sec), leaf count = 40
\[ \left \{ {\it \_C1}+{\frac {4\,{x}^{3}}{3}}-2\,{x}^{2}+4\,x-4\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]