\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a}{y \left ( x \right ) +2\,a \left ( y \left ( x \right ) \right ) ^{4}-16\,{a}^{2}x \left ( y \left ( x \right ) \right ) ^{2}+32\,{a}^{3}{x}^{2}}}=0} \]
Mathematica: cpu = 0.064508 (sec), leaf count = 663 \[ \left \{\left \{y(x)\to -\frac {\sqrt [3]{-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-64 a^4 c_1^2-192 a^3 x\right ){}^3+\left (-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}{12 \sqrt [3]{2} a}+\frac {-64 a^4 c_1^2-192 a^3 x}{6\ 2^{2/3} a \sqrt [3]{-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-64 a^4 c_1^2-192 a^3 x\right ){}^3+\left (-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}+\frac {2 a c_1}{3}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-64 a^4 c_1^2-192 a^3 x\right ){}^3+\left (-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}{24 \sqrt [3]{2} a}-\frac {\left (1+i \sqrt {3}\right ) \left (-64 a^4 c_1^2-192 a^3 x\right )}{12\ 2^{2/3} a \sqrt [3]{-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-64 a^4 c_1^2-192 a^3 x\right ){}^3+\left (-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}+\frac {2 a c_1}{3}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-64 a^4 c_1^2-192 a^3 x\right ){}^3+\left (-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}{24 \sqrt [3]{2} a}-\frac {\left (1-i \sqrt {3}\right ) \left (-64 a^4 c_1^2-192 a^3 x\right )}{12\ 2^{2/3} a \sqrt [3]{-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-64 a^4 c_1^2-192 a^3 x\right ){}^3+\left (-1024 a^6 c_1^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}+\frac {2 a c_1}{3}\right \}\right \} \]
Maple: cpu = 0.046 (sec), leaf count = 864 \[ \left \{ y \left ( x \right ) ={\frac {1}{6\,a}\sqrt [3]{ \left ( 64\,{{ \it \_C1}}^{3}{a}^{4}-576\,{\it \_C1}\,{a}^{3}x+3\,\sqrt {-12288\,{{ \it \_C1}}^{4}{a}^{7}x+24576\,{{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288\,{a }^{5}{x}^{3}+384\,{{\it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+ 81}+27 \right ) {a}^{2}}}-6\,{\frac { \left ( -4/3\,ax-4/9\,{{\it \_C1}} ^{2}{a}^{2} \right ) a}{\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}- 576\,{\it \_C1}\,{a}^{3}x+3\,\sqrt {-12288\,{{\it \_C1}}^{4}{a}^{7}x+ 24576\,{{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{{ \it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{2 }}}}+{\frac {2\,{\it \_C1}\,a}{3}},y \left ( x \right ) =-{\frac {1}{12 \,a}\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}-576\,{\it \_C1}\,{a} ^{3}x+3\,\sqrt {-12288\,{{\it \_C1}}^{4}{a}^{7}x+24576\,{{\it \_C1}}^{ 2}{a}^{6}{x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{{\it \_C1}}^{3}{a}^{4}- 3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{2}}}+3\,{\frac { \left ( -4/3\,ax-4/9\,{{\it \_C1}}^{2}{a}^{2} \right ) a}{\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}-576\,{\it \_C1}\,{a}^{3}x+3\, \sqrt {-12288\,{{\it \_C1}}^{4}{a}^{7}x+24576\,{{\it \_C1}}^{2}{a}^{6} {x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{{\it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{2}}}}+{\frac {2\,{\it \_C1}\,a}{3} }-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{6\,a}\sqrt [3]{ \left ( 64 \,{{\it \_C1}}^{3}{a}^{4}-576\,{\it \_C1}\,{a}^{3}x+3\,\sqrt {-12288\, {{\it \_C1}}^{4}{a}^{7}x+24576\,{{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288\, {a}^{5}{x}^{3}+384\,{{\it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x +81}+27 \right ) {a}^{2}}}+6\,{\frac { \left ( -4/3\,ax-4/9\,{{\it \_C1} }^{2}{a}^{2} \right ) a}{\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}- 576\,{\it \_C1}\,{a}^{3}x+3\,\sqrt {-12288\,{{\it \_C1}}^{4}{a}^{7}x+ 24576\,{{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{{ \it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{2 }}}} \right ) ,y \left ( x \right ) =-{\frac {1}{12\,a}\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}-576\,{\it \_C1}\,{a}^{3}x+3\,\sqrt {-12288 \,{{\it \_C1}}^{4}{a}^{7}x+24576\,{{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288 \,{a}^{5}{x}^{3}+384\,{{\it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3 }x+81}+27 \right ) {a}^{2}}}+3\,{\frac { \left ( -4/3\,ax-4/9\,{{\it \_C1}}^{2}{a}^{2} \right ) a}{\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a} ^{4}-576\,{\it \_C1}\,{a}^{3}x+3\,\sqrt {-12288\,{{\it \_C1}}^{4}{a}^{ 7}x+24576\,{{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{ {\it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{ 2}}}}+{\frac {2\,{\it \_C1}\,a}{3}}+{\frac {i}{2}}\sqrt {3} \left ( { \frac {1}{6\,a}\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}-576\,{ \it \_C1}\,{a}^{3}x+3\,\sqrt {-12288\,{{\it \_C1}}^{4}{a}^{7}x+24576\, {{\it \_C1}}^{2}{a}^{6}{x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{{\it \_C1}} ^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{2}}}+6\,{ \frac { \left ( -4/3\,ax-4/9\,{{\it \_C1}}^{2}{a}^{2} \right ) a}{\sqrt [3]{ \left ( 64\,{{\it \_C1}}^{3}{a}^{4}-576\,{\it \_C1}\,{a}^{3}x+3\, \sqrt {-12288\,{{\it \_C1}}^{4}{a}^{7}x+24576\,{{\it \_C1}}^{2}{a}^{6} {x}^{2}-12288\,{a}^{5}{x}^{3}+384\,{{\it \_C1}}^{3}{a}^{4}-3456\,{\it \_C1}\,{a}^{3}x+81}+27 \right ) {a}^{2}}}} \right ) \right \} \]