\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-x/2-a/2+{x}^{2}\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0} \]
Mathematica: cpu = 0.265034 (sec), leaf count = 42 \[ \left \{\left \{y(x)\to \frac {1}{36} \left (-9 a^2-18 a x-24 c_1 x^3+36 c_1^2+4 x^6-9 x^2\right )\right \}\right \} \]
Maple: cpu = 0.188 (sec), leaf count = 29 \[ \left \{ {\it \_C1}+{\frac {2\,{x}^{3}}{3}}-\sqrt {{x}^{2}+2\,ax+{a}^{ 2}+4\,y \left ( x \right ) }=0 \right \} \]