\[ y'(x)=\frac {2 a}{32 a^3-16 a^2 x y(x)^2+2 a x^2 y(x)^4-x^2 y(x)} \] ✓ Mathematica : cpu = 0.530228 (sec), leaf count = 1347
\[\left \{\left \{y(x)\to -\frac {4 a+e^{c_1}}{12 a}+\frac {\sqrt [3]{4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3+\sqrt {4 \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right ){}^3+\left (4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3\right ){}^2}}}{12 \sqrt [3]{2} a x}-\frac {-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2}{6\ 2^{2/3} a x \sqrt [3]{4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3+\sqrt {4 \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right ){}^3+\left (4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3\right ){}^2}}}\right \},\left \{y(x)\to -\frac {4 a+e^{c_1}}{12 a}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3+\sqrt {4 \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right ){}^3+\left (4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3\right ){}^2}}}{24 \sqrt [3]{2} a x}+\frac {\left (1+i \sqrt {3}\right ) \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right )}{12\ 2^{2/3} a x \sqrt [3]{4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3+\sqrt {4 \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right ){}^3+\left (4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3\right ){}^2}}}\right \},\left \{y(x)\to -\frac {4 a+e^{c_1}}{12 a}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3+\sqrt {4 \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right ){}^3+\left (4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3\right ){}^2}}}{24 \sqrt [3]{2} a x}+\frac {\left (1-i \sqrt {3}\right ) \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right )}{12\ 2^{2/3} a x \sqrt [3]{4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3+\sqrt {4 \left (-192 x a^3-\left (4 a+e^{c_1}\right ){}^2 x^2\right ){}^3+\left (4608 x^2 a^4-128 x^3 a^3+1152 e^{c_1} x^2 a^3-96 e^{c_1} x^3 a^2-432 x^3 a^2-24 e^{2 c_1} x^3 a-2 e^{3 c_1} x^3\right ){}^2}}}\right \}\right \}\] ✓ Maple : cpu = 1.059 (sec), leaf count = 1054
\[\left \{y \left (x \right ) = \frac {-192 c_{1}^{2} a^{3} x -x^{2}-2 \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a \,x^{2}-x^{3}\right )^{\frac {1}{3}} x +\left (-192 i c_{1}^{2} a^{3} x -i x^{2}+i \left (\left (-216 c_{1}^{3} a^{2} x +576 c_{1}^{2} a^{3}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a -x \right ) x^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (\left (-216 c_{1}^{3} a^{2} x +576 c_{1}^{2} a^{3}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a -x \right ) x^{2}\right )^{\frac {2}{3}}}{24 \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a \,x^{2}-x^{3}\right )^{\frac {1}{3}} c_{1} a x}, y \left (x \right ) = -\frac {192 c_{1}^{2} a^{3} x +x^{2}+2 \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a \,x^{2}-x^{3}\right )^{\frac {1}{3}} x +\left (-192 i c_{1}^{2} a^{3} x -i x^{2}+i \left (\left (-216 c_{1}^{3} a^{2} x +576 c_{1}^{2} a^{3}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a -x \right ) x^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (\left (-216 c_{1}^{3} a^{2} x +576 c_{1}^{2} a^{3}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a -x \right ) x^{2}\right )^{\frac {2}{3}}}{24 \left (-216 c_{1}^{3} a^{2} x^{3}+576 c_{1}^{2} a^{3} x^{2}+12 c_{1} \sqrt {\frac {-49152 c_{1}^{4} a^{7}+1536 c_{1}^{2} a^{4} x +\left (324 a^{2} c_{1}^{4}+3 c_{1}\right ) x^{3}+\left (-1728 a^{3} c_{1}^{3}-12 a \right ) x^{2}}{x}}\, a \,x^{2}-x^{3}\right )^{\frac {1}{3}} c_{1} a x}, y \left (x \right ) = \frac {192 c_{1}^{2} a^{3}+x}{12 \left (\left (-216 c_{1}^{3} a^{2} x +576 c_{1}^{2} a^{3}+12 c_{1} \sqrt {-\frac {3 \left (16384 c_{1}^{4} a^{7}-108 a^{2} x^{3} c_{1}^{4}+576 a^{3} x^{2} c_{1}^{3}-512 c_{1}^{2} a^{4} x -x^{3} c_{1}+4 a \,x^{2}\right )}{x}}\, a -x \right ) x^{2}\right )^{\frac {1}{3}} c_{1} a}-\frac {1}{12 c_{1} a}+\frac {\left (\left (-216 c_{1}^{3} a^{2} x +576 c_{1}^{2} a^{3}+12 c_{1} \sqrt {-\frac {3 \left (16384 c_{1}^{4} a^{7}-108 a^{2} x^{3} c_{1}^{4}+576 a^{3} x^{2} c_{1}^{3}-512 c_{1}^{2} a^{4} x -x^{3} c_{1}+4 a \,x^{2}\right )}{x}}\, a -x \right ) x^{2}\right )^{\frac {1}{3}}}{12 c_{1} a x}\right \}\]