\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-x/2-a/2+x\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0} \]
Mathematica: cpu = 0.245531 (sec), leaf count = 40 \[ \left \{\left \{y(x)\to \frac {1}{4} \left (-a^2-2 a x-4 c_1 x^2+4 c_1^2+x^4-x^2\right )\right \}\right \} \]
Maple: cpu = 0.187 (sec), leaf count = 28 \[ \left \{ {\it \_C1}+{x}^{2}+{\frac {1}{2}}-\sqrt {{x}^{2}+2\,ax+{a}^{2 }+4\,y \left ( x \right ) }=0 \right \} \]