\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {2\,a+\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}+{x}^{2}\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}+{x}^{3}\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}}{y \left ( x \right ) }}=0} \]
Mathematica: cpu = 4.434063 (sec), leaf count = 145 \[ \left \{\left \{y(x)\to -\frac {1}{12} \sqrt {576 a x-72 c_1 x^4-96 c_1 x^3-288 c_1 x-144 c_1^2-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4-144 x^2}\right \},\left \{y(x)\to \frac {1}{12} \sqrt {576 a x-72 c_1 x^4-96 c_1 x^3-288 c_1 x-144 c_1^2-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4-144 x^2}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 35 \[ \left \{ -\sqrt {- \left ( y \left ( x \right ) \right ) ^{2}+4\,ax}-{ \frac {{x}^{4}}{4}}-{\frac {{x}^{3}}{3}}-x-{\it \_C1}=0 \right \} \]