\[ y'(x)=\frac {\sqrt {x^2+4 y(x)-4 x}-\frac {x^2}{2}+\frac {x}{2}+1}{x+1} \] ✓ Mathematica : cpu = 0.225455 (sec), leaf count = 40
DSolve[Derivative[1][y][x] == (1 + x/2 - x^2/2 + Sqrt[-4*x + x^2 + 4*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-x^2+4 x+4 \log ^2(x+1)-8 c_1 \log (x+1)+4 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.317 (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))
\[c_{1}+2 \ln \left (1+x \right )-1-\sqrt {x^{2}-4 x +4 y \left (x \right )} = 0\]