\[ y'(x)=x^2 \sqrt {x^2-4 y(x)+2 x+1}+\sqrt {x^2-4 y(x)+2 x+1}+x^3 \sqrt {x^2-4 y(x)+2 x+1}+\frac {x}{2}+\frac {1}{2} \] ✓ Mathematica : cpu = 1.14282 (sec), leaf count = 103
DSolve[Derivative[1][y][x] == 1/2 + x/2 + Sqrt[1 + 2*x + x^2 - 4*y[x]] + x^2*Sqrt[1 + 2*x + x^2 - 4*y[x]] + x^3*Sqrt[1 + 2*x + x^2 - 4*y[x]],y[x],x]
\[\text {Solve}\left [\frac {x^4}{4}+\frac {x^3}{3}+\frac {1}{2} \sqrt {x^2-4 y(x)+2 x+1}+\frac {1}{2} \log \left (\sqrt {x^2-4 y(x)+2 x+1}+x+1\right )-\frac {1}{2} \tanh ^{-1}\left (\frac {2 x+2}{2 \sqrt {x^2-4 y(x)+2 x+1}}\right )-\frac {1}{4} \log (y(x))+x=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.351 (sec), leaf count = 34
dsolve(diff(y(x),x) = 1/2*x+1/2+(x^2+2*x+1-4*y(x))^(1/2)+x^2*(x^2+2*x+1-4*y(x))^(1/2)+x^3*(x^2+2*x+1-4*y(x))^(1/2),y(x))
\[c_{1}-\frac {x^{4}}{2}-\frac {2 x^{3}}{3}-2 x -\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0\]