\[ y'(x)=\frac {2 a}{-16 a^2 x y(x)^2+32 a^3+2 a x^2 y(x)^4-x^2 y(x)} \] ✓ Mathematica : cpu = 0.468192 (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 = 0.869 (sec), leaf count = 1054
\[ \left \{ y \left ( x \right ) ={\frac {1}{24\,{\it \_C1}\,ax} \left ( -2\,x\sqrt [3]{-216\,{{\it \_C1}}^{3}{a}^{2}{x}^{3}+576\,{{\it \_C1}}^{2}{a}^{3}{x}^{2}+12\,a{\it \_C1}\,{x}^{2}\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}-{x}^{3}}+ \left ( -192\,i{{\it \_C1}}^{2}{a}^{3}x+i \left ( \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2} \right ) ^{{\frac {2}{3}}}-i{x}^{2} \right ) \sqrt {3}-192\,{{\it \_C1}}^{2}{a}^{3}x- \left ( \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2} \right ) ^{{\frac {2}{3}}}-{x}^{2} \right ) {\frac {1}{\sqrt [3]{-216\,{{\it \_C1}}^{3}{a}^{2}{x}^{3}+576\,{{\it \_C1}}^{2}{a}^{3}{x}^{2}+12\,a{\it \_C1}\,{x}^{2}\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}-{x}^{3}}}}},y \left ( x \right ) =-{\frac {1}{24\,{\it \_C1}\,ax} \left ( 2\,x\sqrt [3]{-216\,{{\it \_C1}}^{3}{a}^{2}{x}^{3}+576\,{{\it \_C1}}^{2}{a}^{3}{x}^{2}+12\,a{\it \_C1}\,{x}^{2}\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}-{x}^{3}}+ \left ( -192\,i{{\it \_C1}}^{2}{a}^{3}x+i \left ( \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2} \right ) ^{{\frac {2}{3}}}-i{x}^{2} \right ) \sqrt {3}+192\,{{\it \_C1}}^{2}{a}^{3}x+ \left ( \left ( -216\,{{\it \_C1}}^{3}{a}^{2}x+576\,{a}^{3}{{\it \_C1}}^{2}+12\,\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2} \right ) ^{{\frac {2}{3}}}+{x}^{2} \right ) {\frac {1}{\sqrt [3]{-216\,{{\it \_C1}}^{3}{a}^{2}{x}^{3}+576\,{{\it \_C1}}^{2}{a}^{3}{x}^{2}+12\,a{\it \_C1}\,{x}^{2}\sqrt {{\frac { \left ( 324\,{{\it \_C1}}^{4}{a}^{2}+3\,{\it \_C1} \right ) {x}^{3}+ \left ( -1728\,{{\it \_C1}}^{3}{a}^{3}-12\,a \right ) {x}^{2}+1536\,{{\it \_C1}}^{2}{a}^{4}x-49152\,{{\it \_C1}}^{4}{a}^{7}}{x}}}-{x}^{3}}}}},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 {-3\,{\frac {16384\,{{\it \_C1}}^{4}{a}^{7}-108\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+576\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-512\,{{\it \_C1}}^{2}{a}^{4}x-{\it \_C1}\,{x}^{3}+4\,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 {-3\,{\frac {16384\,{{\it \_C1}}^{4}{a}^{7}-108\,{{\it \_C1}}^{4}{a}^{2}{x}^{3}+576\,{{\it \_C1}}^{3}{a}^{3}{x}^{2}-512\,{{\it \_C1}}^{2}{a}^{4}x-{\it \_C1}\,{x}^{3}+4\,a{x}^{2}}{x}}}{\it \_C1}\,a-x \right ) {x}^{2}}}}}-{\frac {1}{12\,{\it \_C1}\,a}} \right \} \]