\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {2\,a+x\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}}{y \left ( x \right ) }}=0} \]
Mathematica: cpu = 1.924244 (sec), leaf count = 101 \[ \left \{\left \{y(x)\to -\frac {\sqrt {4096 a^5 x-256 a^4 x^4+32 a^2 e^{c_1} x^2-e^{2 c_1}}}{32 a^2}\right \},\left \{y(x)\to \frac {\sqrt {4096 a^5 x-256 a^4 x^4+32 a^2 e^{c_1} x^2-e^{2 c_1}}}{32 a^2}\right \}\right \} \]
Maple: cpu = 0.124 (sec), leaf count = 27 \[ \left \{ -\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}-{ \frac {{x}^{2}}{2}}-{\it \_C1}=0 \right \} \]