\[ y'(x)=\frac {2 a \left (4 a x-y(x)^2-1\right )}{128 a^4 x^3-96 a^3 x^2 y(x)^2+24 a^2 x y(x)^4-2 a y(x)^6+4 a x y(x)-y(x)^3-y(x)} \] ✓ Mathematica : cpu = 0.106797 (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 = 0.086 (sec), leaf count = 48
\[ \left \{ {\frac {y \left ( x \right ) }{2\,a}}-{\frac {1}{16\,{a}^{2} \left ( \left ( y \left ( x \right ) \right ) ^{2}-4\,ax \right ) ^{2}}}+ \left ( 32\,{a}^{3}x-8\,{a}^{2} \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{-1}-{\it \_C1}=0 \right \} \]