\[ y'(x)=\frac {\sqrt {x^2+4 y(x)-4 x}-\frac {x^2}{2}+\frac {x}{2}+1}{x+1} \] ✓ Mathematica : cpu = 0.821096 (sec), leaf count = 91
\[\text {Solve}\left [-\frac {1}{2} \sqrt {x^2+4 y(x)-4 x}+\log \left (-\sqrt {x^2+4 y(x)-4 x}-x+2\right )-\tanh ^{-1}\left (\frac {2 x-4}{2 \sqrt {x^2+4 y(x)-4 x}}\right )-\frac {1}{2} \log (2-2 y(x))+\log (x+1)=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.494 (sec), leaf count = 27
\[c_{1}+2 \ln \left (1+x \right )-1-\sqrt {x^{2}-4 x +4 y \relax (x )} = 0\]