\[ y'(x)=x^2 \sqrt {a^2+2 a x+x^2+4 y(x)}+\sqrt {a^2+2 a x+x^2+4 y(x)}+x^3 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.380729 (sec), leaf count = 74
DSolve[Derivative[1][y][x] == -1/2*a - x/2 + Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]] + x^2*Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]] + x^3*Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]],y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{144} \left (-36 a^2-72 a x+9 x^8+24 x^7+16 x^6+72 x^5+96 x^4-72 c_1 x^4-96 c_1 x^3+108 x^2-288 c_1 x+144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.408 (sec), leaf count = 37
dsolve(diff(y(x),x) = -1/2*x-1/2*a+(x^2+2*a*x+a^2+4*y(x))^(1/2)+x^2*(x^2+2*a*x+a^2+4*y(x))^(1/2)+x^3*(x^2+2*a*x+a^2+4*y(x))^(1/2),y(x))
\[c_{1}+\frac {x^{4}}{2}+\frac {2 x^{3}}{3}+2 x -\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )} = 0\]