\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a \left ( x \left ( y \left ( x \right ) \right ) ^{2}-4\,a+x \right ) }{-{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+4\,a{x}^{2}y \left ( x \right ) -{x}^{3}y \left ( x \right ) +2\,a \left ( y \left ( x \right ) \right ) ^{6}{x}^{3}-24\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}{x}^{2}+96\, \left ( y \left ( x \right ) \right ) ^{2}x{a}^{3}-128\,{a}^{4}}}=0} \]
Mathematica: cpu = 1.504191 (sec), leaf count = 401 \[ \left \{\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (64 a^2 c_1 x+2 x^2\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (64 a^2 c_1 x+2 x^2\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (64 a^2 c_1 x+2 x^2\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (64 a^2 c_1 x+2 x^2\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (64 a^2 c_1 x+2 x^2\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,5\right ]\right \}\right \} \]
Maple: cpu = 2.247 (sec), leaf count = 77 \[ \left \{ -{\frac {1}{2\,a} \left ( -{\frac { \left ( y \left ( x \right ) \right ) ^{2}+1}{ \left ( y \left ( x \right ) \right ) ^{4} \left ( x \left ( y \left ( x \right ) \right ) ^{2}-4\,a \right ) }}-2\,{\frac {a }{ \left ( y \left ( x \right ) \right ) ^{4} \left ( x \left ( y \left ( x \right ) \right ) ^{2}-4\,a \right ) ^{2}}} \right ) }+{\frac {1}{4\,{a} ^{2}} \left ( 2\,ay \left ( x \right ) +{\frac {1}{2\, \left ( y \left ( x \right ) \right ) ^{2}}}+{\frac {1}{4\, \left ( y \left ( x \right ) \right ) ^{4}}} \right ) }+{\it \_C1}=0 \right \} \]