\[ y'(x)=\frac {\sqrt {x^2-4 y(x)+2 x+1}+\frac {x^2}{2}+x+\frac {1}{2}}{x+1} \] ✓ Mathematica : cpu = 0.225076 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {1}{4} \left (8 c_1 \log (x+1)-4 c_1^2+x^2+2 x-4 \log ^2(x+1)+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.316 (sec), leaf count = 28
\[ \left \{ {\it \_C1}-2\,\ln \left ( 1+x \right ) -{\frac {1}{2}}-\sqrt {{x}^{2}+2\,x+1-4\,y \left ( x \right ) }=0 \right \} \]