\[ y'(x)=x^2 \sqrt {x^2-4 y(x)+2 x+1}+\sqrt {x^2-4 y(x)+2 x+1}+x^3 \sqrt {x^2-4 y(x)+2 x+1}+\frac {x}{2}+\frac {1}{2} \] ✓ Mathematica : cpu = 0.281587 (sec), leaf count = 69
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]
\[\left \{\left \{y(x)\to \frac {1}{144} \left (-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4+72 c_1 x^4+96 c_1 x^3-108 x^2+72 x+288 c_1 x+36-144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.398 (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))
\[c_{1}-\frac {x^{4}}{2}-\frac {2 x^{3}}{3}-2 x -\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0\]