\[ \boxed { {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +2\,ax{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +ay \left ( x \right ) =0} \]
Mathematica: cpu = 0.009001 (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 = 0.047 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {{\rm Ai}\left (-{ \frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )} \right ) ^{2}+{ \it \_C2}\, \left ( {{\rm Bi}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2} \sqrt [3]{a}}\right )} \right ) ^{2}+{\it \_C3}\,{{\rm Ai}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )}{{\rm Bi}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )} \right \} \]