\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\,a \left ( y \left ( x \right ) \right ) ^{3}+6\,ax \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.241531 (sec), leaf count = 185 \[ \text {Solve}\left [\frac {\sqrt [3]{-3} \sqrt [3]{a} x \text {Ai}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\text {Ai}'\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}{\sqrt [3]{-3} \sqrt [3]{a} x \text {Bi}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\text {Bi}'\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}+c_1=0,y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 48 \[ \left \{ y \left ( x \right ) = \left ( 3\,a{x}^{2}+{\it RootOf} \left ( \sqrt [3]{-3\,a}{{\rm Bi}\left ({\it \_Z}\right )}{\it \_C1}\,x+\sqrt [3 ]{-3\,a}x{{\rm Ai}\left ({\it \_Z}\right )}+{{\rm Bi}^{(1)}\left ({\it \_Z}\right )}{\it \_C1}+{{\rm Ai}^{(1)}\left ({\it \_Z}\right )} \right ) \sqrt [3]{-3\,a} \right ) ^{-1} \right \} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]