\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\, \left ( -\sqrt {a}{x}^{3}+2\,\sqrt {a{x}^{4}+8\,y \left ( x \right ) }+2\,{x}^{2}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }+2\,{x}^{3}\sqrt {a{x}^{4}+8\,y \left ( x \right ) } \right ) \sqrt {a}=0} \]
Mathematica: cpu = 0.493063 (sec), leaf count = 66 \[ \left \{\left \{y(x)\to \frac {1}{72} a \left (-72 c_1 x^4-96 c_1 x^3-288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+87 x^4+144 x^2\right )\right \}\right \} \]
Maple: cpu = 0.327 (sec), leaf count = 38 \[ \left \{ {\frac {1}{4}\sqrt {a{x}^{4}+8\,y \left ( x \right ) }}-\sqrt { a} \left ( {\frac {{x}^{4}}{4}}+{\frac {{x}^{3}}{3}}+x \right ) -{\it \_C1}=0 \right \} \]