\[ y'(x)=\frac {2 a}{32 a^3 x^2-16 a^2 x y(x)^2+2 a y(x)^4+y(x)} \] ✓ Mathematica : cpu = 0.222643 (sec), leaf count = 663
DSolve[Derivative[1][y][x] == (2*a)/(32*a^3*x^2 + y[x] - 16*a^2*x*y[x]^2 + 2*a*y[x]^4),y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt [3]{-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-192 a^3 x-64 a^4 c_1{}^2\right ){}^3+\left (-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}{12 \sqrt [3]{2} a}+\frac {-192 a^3 x-64 a^4 c_1{}^2}{6\ 2^{2/3} a \sqrt [3]{-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-192 a^3 x-64 a^4 c_1{}^2\right ){}^3+\left (-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}+\frac {2 a c_1}{3}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-192 a^3 x-64 a^4 c_1{}^2\right ){}^3+\left (-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}{24 \sqrt [3]{2} a}-\frac {\left (1+i \sqrt {3}\right ) \left (-192 a^3 x-64 a^4 c_1{}^2\right )}{12\ 2^{2/3} a \sqrt [3]{-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-192 a^3 x-64 a^4 c_1{}^2\right ){}^3+\left (-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}+\frac {2 a c_1}{3}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-192 a^3 x-64 a^4 c_1{}^2\right ){}^3+\left (-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}{24 \sqrt [3]{2} a}-\frac {\left (1-i \sqrt {3}\right ) \left (-192 a^3 x-64 a^4 c_1{}^2\right )}{12\ 2^{2/3} a \sqrt [3]{-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2+\sqrt {4 \left (-192 a^3 x-64 a^4 c_1{}^2\right ){}^3+\left (-1024 a^6 c_1{}^3+9216 a^5 c_1 x-432 a^2\right ){}^2}}}+\frac {2 a c_1}{3}\right \}\right \}\] ✓ Maple : cpu = 0.115 (sec), leaf count = 856
dsolve(diff(y(x),x) = 2*a/(y(x)+2*a*y(x)^4-16*a^2*x*y(x)^2+32*a^3*x^2),y(x))
\[y \left (x \right ) = \frac {\left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} x c_{1}^{4}+24576 a^{6} x^{2} c_{1}^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )^{\frac {1}{3}}}{6 a}+\frac {8 a^{2} \left (a c_{1}^{2}+3 x \right )}{3 \left (\left (64 c_{1}^{3} a^{4}-576 c_{1} a^{3} x +3 \sqrt {-12288 a^{7} x c_{1}^{4}+24576 a^{6} x^{2} c_{1}^{2}-12288 a^{5} x^{3}+384 c_{1}^{3} a^{4}-3456 c_{1} a^{3} x +81}+27\right ) a^{2}\right )^{\frac {1}{3}}}+\frac {2 c_{1} a}{3}\]