\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-x/2-a/2+\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }+{x}^{2}\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }+{x}^{3}\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }=0} \]
Mathematica: cpu = 0.500063 (sec), leaf count = 74 \[ \left \{\left \{y(x)\to \frac {1}{144} \left (-36 a^2-72 a x-72 c_1 x^4-96 c_1 x^3-288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+96 x^4+108 x^2\right )\right \}\right \} \]
Maple: cpu = 0.437 (sec), leaf count = 39 \[ \left \{ {\frac {1}{2}\sqrt {{x}^{2}+2\,ax+{a}^{2}+4\,y \left ( x \right ) }}-{\frac {{x}^{4}}{4}}-{\frac {{x}^{3}}{3}}-x-{\it \_C1}=0 \right \} \]