\[ y'(x)=x^2 \sqrt {a^2+2 a x+x^2+4 y(x)}-\frac {a}{2}-\frac {x}{2} \] ✓ Mathematica : cpu = 0.197896 (sec), leaf count = 42
DSolve[Derivative[1][y][x] == -1/2*a - x/2 + x^2*Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]],y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{36} \left (-9 a^2-18 a x+4 x^6-24 c_1 x^3-9 x^2+36 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.247 (sec), leaf count = 29
dsolve(diff(y(x),x) = -1/2*x-1/2*a+x^2*(x^2+2*a*x+a^2+4*y(x))^(1/2),y(x))
\[c_{1}+\frac {2 x^{3}}{3}-\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )} = 0\]