\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac {a}{-{x}^{2}y \left ( x \right ) +2\,a \left ( y \left ( x \right ) \right ) ^{4}{x}^{2}-16\,{a}^{2}x \left ( y \left ( x \right ) \right ) ^{2}+32\,{a}^{3}}}=0} \]
Mathematica: cpu = 0.515566 (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 = 0.561 (sec), leaf count = 1096 \[ \left \{ y \left ( x \right ) ={\frac {1}{12\,{\it \_C1}\,ax}\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12 \,\sqrt {-{\frac {49152\,{{\it \_C1}}^{4}{a}^{7}-324\,{{\it \_C1}}^{4} {a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536\,{{\it \_C1}} ^{2}{a}^{4}x-3\,{\it \_C1}\,{x}^{3}+12\,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}+{\frac {192\,{a}^{3}{{\it \_C1}}^{2}+x}{12\,{\it \_C1}\,a}{\frac {1}{\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+ 576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{\it \_C1}}^{ 4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a }^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1}\,{x}^{3}+12 \,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}}}-{\frac {1}{12\,{ \it \_C1}\,a}},y \left ( x \right ) =-{\frac {1}{24\,{\it \_C1}\,ax} \sqrt [3]{ \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{\it \_C1}}^{4}{a}^{7}-324\,{{ \it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536 \,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1}\,{x}^{3}+12\,a{x}^{2}}{x}}}{ \it \_C1}\,a-x \right ) {x}^{2}}}-{\frac {192\,{a}^{3}{{\it \_C1}}^{2}+ x}{24\,{\it \_C1}\,a}{\frac {1}{\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{ 3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{ \it \_C1}}^{4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1} \,{x}^{3}+12\,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}}}-{ \frac {1}{12\,{\it \_C1}\,a}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1 }{12\,{\it \_C1}\,ax}\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+ 576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{\it \_C1}}^{ 4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a }^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1}\,{x}^{3}+12 \,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}-{\frac {192\,{a}^{3} {{\it \_C1}}^{2}+x}{12\,{\it \_C1}\,a}{\frac {1}{\sqrt [3]{ \left ( - 216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt { -{\frac {49152\,{{\it \_C1}}^{4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x }^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{ 4}x-3\,{\it \_C1}\,{x}^{3}+12\,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) { x}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {1}{24\,{\it \_C1}\,ax }\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{\it \_C1}}^{4}{a}^{7}-324\,{{ \it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536 \,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1}\,{x}^{3}+12\,a{x}^{2}}{x}}}{ \it \_C1}\,a-x \right ) {x}^{2}}}-{\frac {192\,{a}^{3}{{\it \_C1}}^{2}+ x}{24\,{\it \_C1}\,a}{\frac {1}{\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{ 3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{ \it \_C1}}^{4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1} \,{x}^{3}+12\,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}}}-{ \frac {1}{12\,{\it \_C1}\,a}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1 }{12\,{\it \_C1}\,ax}\sqrt [3]{ \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+ 576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {-{\frac {49152\,{{\it \_C1}}^{ 4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+1728\,{{\it \_C1}}^{3}{a }^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{4}x-3\,{\it \_C1}\,{x}^{3}+12 \,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}-{\frac {192\,{a}^{3} {{\it \_C1}}^{2}+x}{12\,{\it \_C1}\,a}{\frac {1}{\sqrt [3]{ \left ( - 216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt { -{\frac {49152\,{{\it \_C1}}^{4}{a}^{7}-324\,{{\it \_C1}}^{4}{a}^{2}{x }^{3}+1728\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-1536\,{{\it \_C1}}^{2}{a}^{ 4}x-3\,{\it \_C1}\,{x}^{3}+12\,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) { x}^{2}}}}} \right ) \right \} \]