\[ 2 a x y'(x)+a y(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0062971 (sec), leaf count = 79
\[\left \{\left \{y(x)\to c_1 \text {Ai}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )^2+c_3 \text {Bi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )^2+c_2 \text {Ai}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right ) \text {Bi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.053 (sec), leaf count = 55
\[y \relax (x ) = c_{1} \AiryAi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+c_{2} \AiryBi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+c_{3} \AiryAi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right ) \AiryBi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )\]