\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( y \left ( x \right ) \right ) ^{3}+ax \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.227029 (sec), leaf count = 195 \[ \text {Solve}\left [\frac {\text {Ai}'\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \text {Ai}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}{\text {Bi}'\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )-\left (-\frac {1}{2}\right )^{2/3} a^{2/3} x \text {Bi}\left (\frac {\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a}}{y(x)}-\frac {1}{2} \sqrt [3]{-\frac {1}{2}} a^{4/3} x^2\right )}+c_1=0,y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 62 \[ \left \{ y \left ( x \right ) =2\,{\frac {a}{{a}^{2}{x}^{2}+2\,{\it RootOf} \left ( \sqrt [3]{-2\,{a}^{2}}{{\rm Bi}\left ({\it \_Z}\right )}{ \it \_C1}\,x+\sqrt [3]{-2\,{a}^{2}}x{{\rm Ai}\left ({\it \_Z}\right )}+2 \,{{\rm Bi}^{(1)}\left ({\it \_Z}\right )}{\it \_C1}+2\,{{\rm Ai}^{(1 )}\left ({\it \_Z}\right )} \right ) \sqrt [3]{-2\,{a}^{2}}}} \right \} \]
Sage: cpu = 0 (sec), leaf count = 0 \[ \text {Maxima was unable to solve this ODE} \]