\[ y'(x)=\frac {\frac {x^2}{2}+x^3 \sqrt {x^2-4 y(x)+2 x+1}+x+\frac {1}{2}}{x+1} \] ✓ Mathematica : cpu = 0.453364 (sec), leaf count = 105
\[\left \{\left \{y(x)\to \frac {1}{36} \left (-4 x^6+12 x^5-33 x^4+36 x^3+24 x^3 \log (x+1)+24 c_1 x^3-27 x^2-36 x^2 \log (x+1)-36 c_1 x^2+18 x-36 \log ^2(x+1)+72 x \log (x+1)+72 c_1 x-72 c_1 \log (x+1)+9-36 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.538 (sec), leaf count = 38
\[c_{1}-\frac {2 x^{3}}{3}+x^{2}-2 x +2 \ln \left (1+x \right )-\sqrt {x^{2}+2 x +1-4 y \relax (x )} = 0\]