\[ y'(x)=\frac {\sqrt {x^2-4 y(x)+2 x+1}+\frac {x^2}{2}+x+\frac {1}{2}}{x+1} \] ✓ Mathematica : cpu = 0.713266 (sec), leaf count = 89
\[\text {Solve}\left [\frac {1}{2} \left (\sqrt {x^2-4 y(x)+2 x+1}+\log \left (\sqrt {x^2-4 y(x)+2 x+1}+x+1\right )-\tanh ^{-1}\left (\frac {2 x+2}{2 \sqrt {x^2-4 y(x)+2 x+1}}\right )+2 \log (x+1)\right )-\frac {1}{4} \log (y(x))=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.615 (sec), leaf count = 28
\[ \left \{ {\it \_C1}-2\,\ln \left ( 1+x \right ) -{\frac {1}{2}}-\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0 \right \} \]