\[ y'(x)=\frac {-\frac {x^2}{2}+x^3 \sqrt {x^2+4 y(x)-4 x}+\frac {x}{2}+1}{x+1} \] ✓ Mathematica : cpu = 0.474216 (sec), leaf count = 104
DSolve[Derivative[1][y][x] == (1 + x/2 - x^2/2 + x^3*Sqrt[-4*x + x^2 + 4*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{36} \left (4 x^6-12 x^5+33 x^4-36 x^3-24 x^3 \log (x+1)-24 c_1 x^3+27 x^2+36 x^2 \log (x+1)+36 c_1 x^2+36 x+36 \log ^2(x+1)-72 x \log (x+1)-72 c_1 x+72 c_1 \log (x+1)+36 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.501 (sec), leaf count = 39
dsolve(diff(y(x),x) = 1/2*(-x^2+x+2+2*x^3*(x^2-4*x+4*y(x))^(1/2))/(1+x),y(x))
\[c_{1}+\frac {2 x^{3}}{3}-x^{2}+2 x -2 \ln \left (1+x \right )-\sqrt {x^{2}-4 x +4 y \left (x \right )} = 0\]