\[ y'(x)=\frac {2 a \left (4 a x-y(x)^2-1\right )}{128 a^4 x^3-96 a^3 x^2 y(x)^2+24 a^2 x y(x)^4-2 a y(x)^6+4 a x y(x)-y(x)^3-y(x)} \] ✓ Mathematica : cpu = 0.185562 (sec), leaf count = 381
\[\left \{\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a-16 \text {$\#$1}^4 a^2 c_1-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (-2+128 a^3 c_1 x\right )+128 \text {$\#$1} a^3 x^2-256 a^4 c_1 x^2+8 a x-1\& ,5\right ]\right \}\right \}\] ✓ Maple : cpu = 0.064 (sec), leaf count = 48
\[\frac {y \relax (x )}{2 a}-\frac {1}{16 a^{2} \left (y \relax (x )^{2}-4 a x \right )^{2}}+\frac {1}{32 a^{3} x -8 a^{2} y \relax (x )^{2}}-c_{1} = 0\]