\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a \left ( - \left ( y \left ( x \right ) \right ) ^{2}+4\,ax-1 \right ) }{- \left ( y \left ( x \right ) \right ) ^{3}+4\,axy \left ( x \right ) -y \left ( x \right ) -2\,a \left ( y \left ( x \right ) \right ) ^{6}+24\, \left ( y \left ( x \right ) \right ) ^{4}{a}^{2}x-96\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{3}{x}^{2}+128\,{a}^{4}{x}^{3}}}=0} \]
Mathematica: cpu = 0.091011 (sec), leaf count = 381 \[ \left \{\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (128 a^3 c_1 x-2\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (128 a^3 c_1 x-2\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (128 a^3 c_1 x-2\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (128 a^3 c_1 x-2\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (128 a^3 c_1 x-2\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,5\right ]\right \}\right \} \]
Maple: cpu = 0.063 (sec), leaf count = 46 \[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}-{\frac {1}{8\,{a}^{2} \left ( \left ( y \left ( x \right ) \right ) ^{2}-4\,ax \right ) }}-{ \frac {1}{16\,{a}^{2} \left ( \left ( y \left ( x \right ) \right ) ^{2}- 4\,ax \right ) ^{2}}}-{\it \_C1}=0 \right \} \]