\[ y'(x)=\frac {2 a \left (-4 a+x y(x)^2+x\right )}{-128 a^4+96 a^3 x y(x)^2-24 a^2 x^2 y(x)^4+2 a x^3 y(x)^6+4 a x^2 y(x)-x^3 y(x)^3-x^3 y(x)} \] ✓ Mathematica : cpu = 1.00516 (sec), leaf count = 401
\[\left \{\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,1\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,2\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,3\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,4\right ]\right \},\left \{y(x)\to \text {Root}\left [8 \text {$\#$1}^5 a x^2-8 \text {$\#$1}^4 a c_1 x^2-64 \text {$\#$1}^3 a^2 x+\text {$\#$1}^2 \left (2 x^2+64 a^2 c_1 x\right )+128 \text {$\#$1} a^3-128 a^3 c_1-8 a x+x^2\& ,5\right ]\right \}\right \}\] ✓ Maple : cpu = 5.042 (sec), leaf count = 71
\[\frac {x y \relax (x )^{4}+\left (-4 a +x \right ) y \relax (x )^{2}-2 a}{2 a y \relax (x )^{4} \left (-x y \relax (x )^{2}+4 a \right )^{2}}+\frac {8 a y \relax (x )^{5}+2 y \relax (x )^{2}+1}{16 a^{2} y \relax (x )^{4}}+c_{1} = 0\]