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