\[ \boxed { {x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a \left ( y \left ( x \right ) \right ) ^{3}-a{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0.390050 (sec), leaf count = 267 \[ \text {Solve}\left [\frac {\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \text {Ai}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\text {Ai}'\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}{\left (-\frac {1}{2^{2/3} a^{2/3} y(x)}-\frac {\sqrt [3]{a} x}{2^{2/3}}\right ) \text {Bi}\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )+\text {Bi}'\left (\left (-\frac {\sqrt [3]{a} x}{2^{2/3}}-\frac {1}{2^{2/3} a^{2/3} y(x)}\right )^2+\frac {1}{\sqrt [3]{2} \sqrt [3]{a} x}\right )}+c_1=0,y(x)\right ] \]
Maple: cpu = 0.078 (sec), leaf count = 117 \[ \left \{ y \left ( x \right ) =- \left ( ax+ \left ( -2\,a \right ) ^{{ \frac {2}{3}}}{\it RootOf} \left ( {{\rm Bi}\left ({\frac {1}{x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a} }}}\right )}{\it \_C1}\,{\it \_Z}+{\it \_Z}\,{{\rm Ai}\left ({\frac {1}{ x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}}\right )}+{{\rm Bi}^{(1)}\left ({\frac {1}{x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}} \right )}{\it \_C1}+{{\rm Ai}^{(1)}\left ({\frac {1}{x} \left ( {{\it \_Z }}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}} \right )} \right ) \right ) ^{-1} \right \} \]