\[ -a x^2 y(x)^2+a y(x)^3+x^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.654849 (sec), leaf count = 239
\[\text {Solve}\left [\frac {\text {Ai}'\left (\frac {2 a y(x) x^2+x+a \left (a x^3+2\right ) y(x)^2}{2 \sqrt [3]{2} a^{4/3} x y(x)^2}\right )-\frac {(a x y(x)+1) \text {Ai}\left (\frac {2 a y(x) x^2+x+a \left (a x^3+2\right ) y(x)^2}{2 \sqrt [3]{2} a^{4/3} x y(x)^2}\right )}{2^{2/3} a^{2/3} y(x)}}{\text {Bi}'\left (\frac {2 a y(x) x^2+x+a \left (a x^3+2\right ) y(x)^2}{2 \sqrt [3]{2} a^{4/3} x y(x)^2}\right )-\frac {(a x y(x)+1) \text {Bi}\left (\frac {2 a y(x) x^2+x+a \left (a x^3+2\right ) y(x)^2}{2 \sqrt [3]{2} a^{4/3} x y(x)^2}\right )}{2^{2/3} a^{2/3} y(x)}}+c_1=0,y(x)\right ]\]
✓ Maple : cpu = 0.122 (sec), leaf count = 117
\[ \left \{ y \left ( x \right ) =- \left ( ax+ \left ( -2\,a \right ) ^{{\frac {2}{3}}}{\it RootOf} \left ( {{\rm Bi}\left ({\frac {1}{x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}}\right )}{\it \_C1}\,{\it \_Z}+{\it \_Z}\,{{\rm Ai}\left ({\frac {1}{x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}}\right )}+{{\rm Bi}^{(1)}\left ({\frac {1}{x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}}\right )}{\it \_C1}+{{\rm Ai}^{(1)}\left ({\frac {1}{x} \left ( {{\it \_Z}}^{2}\sqrt [3]{-2\,a}x-1 \right ) {\frac {1}{\sqrt [3]{-2\,a}}}}\right )} \right ) \right ) ^{-1} \right \} \]