\[ a x^2 y(x)^3+b y(x)^2+x^2 y'(x)=0 \] ✓ Mathematica : cpu = 0.956268 (sec), leaf count = 343
\[\text {Solve}\left [\frac {\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Ai}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\text {Ai}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}{\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} \sqrt [3]{b} y(x)}\right ) \text {Bi}\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )+\text {Bi}'\left (\left (\frac {b^{2/3}}{2^{2/3} \sqrt [3]{a} x}+\frac {1}{2^{2/3} \sqrt [3]{a} y(x) \sqrt [3]{b}}\right )^2-\frac {\sqrt [3]{a} x}{\sqrt [3]{2} b^{2/3}}\right )}+c_1=0,y(x)\right ]\] ✓ Maple : cpu = 0.206 (sec), leaf count = 178
\[\left \{y \left (x \right ) = -\frac {2^{\frac {1}{3}} a b x}{2^{\frac {1}{3}} a \,b^{2}-2 \left (a^{2} b^{2}\right )^{\frac {2}{3}} x \RootOf \left (c_{1} \textit {\_Z} \AiryBi \left (-\frac {-2 \left (a^{2} b^{2}\right )^{\frac {1}{3}} \textit {\_Z}^{2}+2^{\frac {2}{3}} a x}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )+c_{1} \AiryBi \left (1, -\frac {-2 \left (a^{2} b^{2}\right )^{\frac {1}{3}} \textit {\_Z}^{2}+2^{\frac {2}{3}} a x}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )+\textit {\_Z} \AiryAi \left (-\frac {-2 \left (a^{2} b^{2}\right )^{\frac {1}{3}} \textit {\_Z}^{2}+2^{\frac {2}{3}} a x}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )+\AiryAi \left (1, -\frac {-2 \left (a^{2} b^{2}\right )^{\frac {1}{3}} \textit {\_Z}^{2}+2^{\frac {2}{3}} a x}{2 \left (a^{2} b^{2}\right )^{\frac {1}{3}}}\right )\right )}\right \}\]