\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,a{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}+2\,xy \left ( x \right ) =0} \]
Mathematica: cpu = 0.014502 (sec), leaf count = 72 \[ \left \{\left \{y(x)\to -\frac {\sqrt {2}}{\sqrt {-2 a x^2-a+2 c_1 e^{2 x^2}}}\right \},\left \{y(x)\to \frac {\sqrt {2}}{\sqrt {-2 a x^2-a+2 c_1 e^{2 x^2}}}\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) =-2\,{\frac {1}{\sqrt {-4\,a{x}^{2}+4\,{ {\rm e}^{2\,{x}^{2}}}{\it \_C1}-2\,a}}},y \left ( x \right ) =2\,{\frac {1}{\sqrt {-4\,a{x}^{2}+4\,{{\rm e}^{2\,{x}^{2}}}{\it \_C1}-2\,a}}} \right \} \]
Sage: cpu = 0.9 (sec), leaf count = 0 \[ \left [\frac {e^{\left (-x^{2}\right )}}{\sqrt {-\frac {1}{2} \, {\left (2 \, x^{2} + 1\right )} a e^{\left (-2 \, x^{2}\right )} + c}}, \text {\texttt {bernoulli}}\right ] \]