\[ y'(x)=\frac {x^3 \sqrt {x^2-4 y(x)+2 x+1}+\frac {x^2}{2}+x+\frac {1}{2}}{x+1} \] ✓ Mathematica : cpu = 0.446107 (sec), leaf count = 105
\[\left \{\left \{y(x)\to \frac {1}{36} \left (-4 x^6+12 x^5-33 x^4+36 x^3-27 x^2+24 x^3 \log (x+1)-36 x^2 \log (x+1)+24 c_1 x^3-36 c_1 x^2+18 x-36 \log ^2(x+1)+72 x \log (x+1)+72 c_1 x-72 c_1 \log (x+1)+9-36 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.668 (sec), leaf count = 38
\[ \left \{ {\it \_C1}-{\frac {2\,{x}^{3}}{3}}+{x}^{2}-2\,x+2\,\ln \left ( 1+x \right ) -\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0 \right \} \]