\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =4\,{\frac {x \left ( a-1 \right ) \left ( a+1 \right ) }{4\,y \left ( x \right ) +{a}^{2} \left ( y \left ( x \right ) \right ) ^{4}-2\,{a}^{4} \left ( y \left ( x \right ) \right ) ^{2}{x}^{2}+4\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}{x}^{2}+{a}^{6}{x}^{4}-3\,{a}^{4}{x}^{4}+3\,{a}^{2}{x}^{4}- \left ( y \left ( x \right ) \right ) ^{4}-2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{x}^{4}}}=0} \]
Mathematica: cpu = 1.364673 (sec), leaf count = 1278 \[ \left \{\left \{y(x)\to -\frac {c_1}{3 \left (1-a^2\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 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-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 (1-a^2\right )}-\frac {\sqrt [3]{2} \left (3 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-c_1^2\right )}{3 \left (1-a^2\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 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-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 (1-a^2\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 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-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 (1-a^2\right )}+\frac {\left (1+i \sqrt {3}\right ) \left (3 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-c_1^2\right )}{3\ 2^{2/3} \left (1-a^2\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 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-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 (1-a^2\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 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-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 (1-a^2\right )}+\frac {\left (1-i \sqrt {3}\right ) \left (3 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-c_1^2\right )}{3\ 2^{2/3} \left (1-a^2\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 \left (1-a^2\right ) \left (x^2 a^4-2 x^2 a^2+x^2\right )-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 = 0.312 (sec), leaf count = 1742 \[ \left \{ y \left ( x \right ) =-{\frac {{9}^{{\frac {2}{3}}}}{54\,{a}^{2 }-54} \left ( \left ( 2\,{\it \_C1}\,{a}^{2}-2\,{\it \_C1} \right ) \sqrt [3]{9}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {\frac {1}{3}\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1}\, \left ( a-1 \right ) ^{2 } \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}}^{3}{a}^{2}-{{\it \_C1}}^ {3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{\it \_C1}}^{3}+ 81}}+3+ \left ( -{\frac {{a}^{2}}{9}}+{\frac {1}{9}} \right ) {{\it \_C1 }}^{3}+{x}^{2} \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2}{\it \_C1} \right ) }+ \left ( -3\,i{a}^{6}{x}^{2}+ \left ( 9\,i{x}^{2}-i{{ \it \_C1}}^{2} \right ) {a}^{4}+ \left ( -9\,i{x}^{2}+2\,i{{\it \_C1}}^{ 2} \right ) {a}^{2}+i \left ( \left ( 9\,{x}^{2}{\it \_C1}\,{a}^{4}-{{ \it \_C1}}^{3}{a}^{2}-18\,{\it \_C1}\,{a}^{2}{x}^{2}+{{\it \_C1}}^{3}+ 9\,{\it \_C1}\,{x}^{2}+3\,\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a +1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1}\, \left ( a-1 \right ) ^{2 } \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}}^{3}{a}^{2}-{{\it \_C1}}^ {3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{\it \_C1}}^{3}+ 81}+27 \right ) \left ( {a}^{2}-1 \right ) ^{2} \right ) ^{{\frac {2}{3}} }+3\,i{x}^{2}-i{{\it \_C1}}^{2} \right ) \sqrt {3}+3\,{a}^{6}{x}^{2}+ \left ( {{\it \_C1}}^{2}-9\,{x}^{2} \right ) {a}^{4}+ \left ( -2\,{{\it \_C1}}^{2}+9\,{x}^{2} \right ) {a}^{2}+ \left ( \left ( 9\,{x}^{2}{\it \_C1}\,{a}^{4}-{{\it \_C1}}^{3}{a}^{2}-18\,{\it \_C1}\,{a}^{2}{x}^{2}+ {{\it \_C1}}^{3}+9\,{\it \_C1}\,{x}^{2}+3\,\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1} \, \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}} ^{3}{a}^{2}-{{\it \_C1}}^{3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a} ^{2}+6\,{{\it \_C1}}^{3}+81}+27 \right ) \left ( {a}^{2}-1 \right ) ^{2} \right ) ^{{\frac {2}{3}}}-3\,{x}^{2}+{{\it \_C1}}^{2} \right ) {\frac {1}{\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {\frac {1}{3}\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{ 5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1}\, \left ( a-1 \right ) ^{2} \left ( a+ 1 \right ) ^{2} \left ( {{\it \_C1}}^{3}{a}^{2}-{{\it \_C1}}^{3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{\it \_C1}}^{3}+81}}+3 + \left ( -{\frac {{a}^{2}}{9}}+{\frac {1}{9}} \right ) {{\it \_C1}}^{3} +{x}^{2} \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2}{\it \_C1} \right ) }}}},y \left ( x \right ) ={\frac {{9}^{{\frac {2}{3}}}}{27\,{a }^{2}-27} \left ( \left ( -{\it \_C1}\,{a}^{2}+{\it \_C1} \right ) \sqrt [3]{9}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {\frac {1}{3}\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1}\, \left ( a-1 \right ) ^{2 } \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}}^{3}{a}^{2}-{{\it \_C1}}^ {3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{\it \_C1}}^{3}+ 81}}+3+ \left ( -{\frac {{a}^{2}}{9}}+{\frac {1}{9}} \right ) {{\it \_C1 }}^{3}+{x}^{2} \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2}{\it \_C1} \right ) }+3\,{a}^{6}{x}^{2}+ \left ( {{\it \_C1}}^{2}-9\,{x}^{2} \right ) {a}^{4}+ \left ( -2\,{{\it \_C1}}^{2}+9\,{x}^{2} \right ) {a}^{ 2}+ \left ( \left ( 9\,{x}^{2}{\it \_C1}\,{a}^{4}-{{\it \_C1}}^{3}{a}^{ 2}-18\,{\it \_C1}\,{a}^{2}{x}^{2}+{{\it \_C1}}^{3}+9\,{\it \_C1}\,{x}^ {2}+3\,\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^ {6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4 }{x}^{4}-3\,{\it \_C1}\, \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{ 2} \left ( {{\it \_C1}}^{3}{a}^{2}-{{\it \_C1}}^{3}-18 \right ) {x}^{2}- 6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{\it \_C1}}^{3}+81}+27 \right ) \left ( {a}^{2}-1 \right ) ^{2} \right ) ^{{\frac {2}{3}}}-3\,{x}^{2}+{{\it \_C1 }}^{2} \right ) {\frac {1}{\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( a+ 1 \right ) ^{2} \left ( {\frac {1}{3}\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1}\, \left ( a- 1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}}^{3}{a}^{2}- {{\it \_C1}}^{3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{ \it \_C1}}^{3}+81}}+3+ \left ( -{\frac {{a}^{2}}{9}}+{\frac {1}{9}} \right ) {{\it \_C1}}^{3}+{x}^{2} \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2}{\it \_C1} \right ) }}}},y \left ( x \right ) ={\frac {{9}^{ {\frac {2}{3}}}}{54\,{a}^{2}-54} \left ( \left ( -2\,{\it \_C1}\,{a}^{2 }+2\,{\it \_C1} \right ) \sqrt [3]{9}\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {\frac {1}{3}\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1} \, \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}} ^{3}{a}^{2}-{{\it \_C1}}^{3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a} ^{2}+6\,{{\it \_C1}}^{3}+81}}+3+ \left ( -{\frac {{a}^{2}}{9}}+{\frac { 1}{9}} \right ) {{\it \_C1}}^{3}+{x}^{2} \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2}{\it \_C1} \right ) }+ \left ( -3\,i{a}^{6}{x}^{ 2}+ \left ( 9\,i{x}^{2}-i{{\it \_C1}}^{2} \right ) {a}^{4}+ \left ( -9\,i {x}^{2}+2\,i{{\it \_C1}}^{2} \right ) {a}^{2}+i \left ( \left ( 9\,{x}^{ 2}{\it \_C1}\,{a}^{4}-{{\it \_C1}}^{3}{a}^{2}-18\,{\it \_C1}\,{a}^{2}{ x}^{2}+{{\it \_C1}}^{3}+9\,{\it \_C1}\,{x}^{2}+3\,\sqrt {-3\, \left ( a -1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1} \, \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}} ^{3}{a}^{2}-{{\it \_C1}}^{3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a} ^{2}+6\,{{\it \_C1}}^{3}+81}+27 \right ) \left ( {a}^{2}-1 \right ) ^{2} \right ) ^{{\frac {2}{3}}}+3\,i{x}^{2}-i{{\it \_C1}}^{2} \right ) \sqrt {3}-3\,{a}^{6}{x}^{2}+ \left ( -{{\it \_C1}}^{2}+9\,{x}^{2} \right ) {a}^{4}+ \left ( 2\,{{\it \_C1}}^{2}-9\,{x}^{2} \right ) {a}^{2 }- \left ( \left ( 9\,{x}^{2}{\it \_C1}\,{a}^{4}-{{\it \_C1}}^{3}{a}^{2 }-18\,{\it \_C1}\,{a}^{2}{x}^{2}+{{\it \_C1}}^{3}+9\,{\it \_C1}\,{x}^{ 2}+3\,\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{ 6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4} {x}^{4}-3\,{\it \_C1}\, \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2 } \left ( {{\it \_C1}}^{3}{a}^{2}-{{\it \_C1}}^{3}-18 \right ) {x}^{2}-6 \,{{\it \_C1}}^{3}{a}^{2}+6\,{{\it \_C1}}^{3}+81}+27 \right ) \left ( { a}^{2}-1 \right ) ^{2} \right ) ^{{\frac {2}{3}}}+3\,{x}^{2}-{{\it \_C1} }^{2} \right ) {\frac {1}{\sqrt [3]{ \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {\frac {1}{3}\sqrt {-3\, \left ( a-1 \right ) ^{5} \left ( a+1 \right ) ^{5}{x}^{6}+6\,{{\it \_C1}}^{2} \left ( a-1 \right ) ^{4} \left ( a+1 \right ) ^{4}{x}^{4}-3\,{\it \_C1}\, \left ( a- 1 \right ) ^{2} \left ( a+1 \right ) ^{2} \left ( {{\it \_C1}}^{3}{a}^{2}- {{\it \_C1}}^{3}-18 \right ) {x}^{2}-6\,{{\it \_C1}}^{3}{a}^{2}+6\,{{ \it \_C1}}^{3}+81}}+3+ \left ( -{\frac {{a}^{2}}{9}}+{\frac {1}{9}} \right ) {{\it \_C1}}^{3}+{x}^{2} \left ( a-1 \right ) ^{2} \left ( a+1 \right ) ^{2}{\it \_C1} \right ) }}}} \right \} \]