\[ y'(x)=\frac {4 (a-1) (a+1) x}{a^6 x^4-3 a^4 x^4-2 a^4 x^2 y(x)^2+3 a^2 x^4+4 a^2 x^2 y(x)^2+a^2 y(x)^4-x^4-2 x^2 y(x)^2-y(x)^4+4 y(x)} \] ✓ Mathematica : cpu = 1.14253 (sec), leaf count = 1269
\[\left \{\left \{y(x)\to \frac {c_1}{3 \left (a^2-1\right )}+\frac {\sqrt [3]{-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+\sqrt {4 \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right ){}^3+\left (-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+54\right ){}^2}+54}}{3 \sqrt [3]{2} \left (a^2-1\right )}-\frac {\sqrt [3]{2} \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right )}{3 \left (a^2-1\right ) \sqrt [3]{-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+\sqrt {4 \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right ){}^3+\left (-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+54\right ){}^2}+54}}\right \},\left \{y(x)\to \frac {c_1}{3 \left (a^2-1\right )}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+\sqrt {4 \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right ){}^3+\left (-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+54\right ){}^2}+54}}{6 \sqrt [3]{2} \left (a^2-1\right )}+\frac {\left (1+i \sqrt {3}\right ) \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right )}{3\ 2^{2/3} \left (a^2-1\right ) \sqrt [3]{-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+\sqrt {4 \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right ){}^3+\left (-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+54\right ){}^2}+54}}\right \},\left \{y(x)\to \frac {c_1}{3 \left (a^2-1\right )}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+\sqrt {4 \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right ){}^3+\left (-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+54\right ){}^2}+54}}{6 \sqrt [3]{2} \left (a^2-1\right )}+\frac {\left (1-i \sqrt {3}\right ) \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right )}{3\ 2^{2/3} \left (a^2-1\right ) \sqrt [3]{-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+\sqrt {4 \left (-3 x^2 a^6+9 x^2 a^4-9 x^2 a^2+3 x^2-c_1{}^2\right ){}^3+\left (-18 x^2 c_1 a^6+54 x^2 c_1 a^4+54 a^4-54 x^2 c_1 a^2-108 a^2+2 c_1{}^3+18 x^2 c_1+54\right ){}^2}+54}}\right \}\right \}\] ✓ Maple : cpu = 0.343 (sec), leaf count = 1742
\[\left \{y \left (x \right ) = \frac {9^{\frac {2}{3}} \left (3 a^{6} x^{2}+\left (-9 x^{2}+c_{1}^{2}\right ) a^{4}+c_{1}^{2}+\left (9 x^{2}-2 c_{1}^{2}\right ) a^{2}-3 x^{2}+\left (-c_{1} a^{2}+c_{1}\right ) 9^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (a +1\right )^{2} \left (\left (-\frac {a^{2}}{9}+\frac {1}{9}\right ) c_{1}^{3}+c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} x^{2}+\frac {\sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}}{3}+3\right )\right )^{\frac {1}{3}}+\left (\left (9 c_{1} a^{4} x^{2}-c_{1}^{3} a^{2}-18 c_{1} a^{2} x^{2}+c_{1}^{3}+9 c_{1} x^{2}+3 \sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}+27\right ) \left (a^{2}-1\right )^{2}\right )^{\frac {2}{3}}\right )}{9 \left (\left (a -1\right )^{2} \left (a +1\right )^{2} \left (\left (-\frac {a^{2}}{9}+\frac {1}{9}\right ) c_{1}^{3}+c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} x^{2}+\frac {\sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}}{3}+3\right )\right )^{\frac {1}{3}} \left (3 a^{2}-3\right )}, y \left (x \right ) = \frac {\left (-3 a^{6} x^{2}+\left (9 x^{2}-c_{1}^{2}\right ) a^{4}-c_{1}^{2}+\left (-9 x^{2}+2 c_{1}^{2}\right ) a^{2}+3 x^{2}+\left (-2 c_{1} a^{2}+2 c_{1}\right ) 9^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (a +1\right )^{2} \left (\left (-\frac {a^{2}}{9}+\frac {1}{9}\right ) c_{1}^{3}+c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} x^{2}+\frac {\sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}}{3}+3\right )\right )^{\frac {1}{3}}+\left (-3 i a^{6} x^{2}+\left (9 i x^{2}-i c_{1}^{2}\right ) a^{4}-i c_{1}^{2}+\left (-9 i x^{2}+2 i c_{1}^{2}\right ) a^{2}+3 i x^{2}+i \left (\left (9 c_{1} a^{4} x^{2}-c_{1}^{3} a^{2}-18 c_{1} a^{2} x^{2}+c_{1}^{3}+9 c_{1} x^{2}+3 \sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}+27\right ) \left (a^{2}-1\right )^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (\left (9 c_{1} a^{4} x^{2}-c_{1}^{3} a^{2}-18 c_{1} a^{2} x^{2}+c_{1}^{3}+9 c_{1} x^{2}+3 \sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}+27\right ) \left (a^{2}-1\right )^{2}\right )^{\frac {2}{3}}\right ) 9^{\frac {2}{3}}}{9 \left (\left (a -1\right )^{2} \left (a +1\right )^{2} \left (\left (-\frac {a^{2}}{9}+\frac {1}{9}\right ) c_{1}^{3}+c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} x^{2}+\frac {\sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}}{3}+3\right )\right )^{\frac {1}{3}} \left (6 a^{2}-6\right )}, y \left (x \right ) = -\frac {\left (3 a^{6} x^{2}+\left (-9 x^{2}+c_{1}^{2}\right ) a^{4}+c_{1}^{2}+\left (9 x^{2}-2 c_{1}^{2}\right ) a^{2}-3 x^{2}+\left (2 c_{1} a^{2}-2 c_{1}\right ) 9^{\frac {1}{3}} \left (\left (a -1\right )^{2} \left (a +1\right )^{2} \left (\left (-\frac {a^{2}}{9}+\frac {1}{9}\right ) c_{1}^{3}+c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} x^{2}+\frac {\sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}}{3}+3\right )\right )^{\frac {1}{3}}+\left (-3 i a^{6} x^{2}+\left (9 i x^{2}-i c_{1}^{2}\right ) a^{4}-i c_{1}^{2}+\left (-9 i x^{2}+2 i c_{1}^{2}\right ) a^{2}+3 i x^{2}+i \left (\left (9 c_{1} a^{4} x^{2}-c_{1}^{3} a^{2}-18 c_{1} a^{2} x^{2}+c_{1}^{3}+9 c_{1} x^{2}+3 \sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}+27\right ) \left (a^{2}-1\right )^{2}\right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (\left (9 c_{1} a^{4} x^{2}-c_{1}^{3} a^{2}-18 c_{1} a^{2} x^{2}+c_{1}^{3}+9 c_{1} x^{2}+3 \sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}+27\right ) \left (a^{2}-1\right )^{2}\right )^{\frac {2}{3}}\right ) 9^{\frac {2}{3}}}{9 \left (\left (a -1\right )^{2} \left (a +1\right )^{2} \left (\left (-\frac {a^{2}}{9}+\frac {1}{9}\right ) c_{1}^{3}+c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} x^{2}+\frac {\sqrt {6 \left (a -1\right )^{4} \left (a +1\right )^{4} c_{1}^{2} x^{4}-3 \left (a -1\right )^{5} \left (a +1\right )^{5} x^{6}-6 c_{1}^{3} a^{2}+6 c_{1}^{3}-3 c_{1} \left (a -1\right )^{2} \left (a +1\right )^{2} \left (c_{1}^{3} a^{2}-c_{1}^{3}-18\right ) x^{2}+81}}{3}+3\right )\right )^{\frac {1}{3}} \left (6 a^{2}-6\right )}\right \}\]