\[ 2 a x y'(x)+a y(x)+y^{(3)}(x)=0 \] ✓ Mathematica : cpu = 0.0056465 (sec), leaf count = 79
DSolve[a*y[x] + 2*a*x*Derivative[1][y][x] + Derivative[3][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {AiryAi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )^2+c_3 \operatorname {AiryBi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )^2+c_2 \operatorname {AiryAi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right ) \operatorname {AiryBi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.039 (sec), leaf count = 55
dsolve(diff(diff(diff(y(x),x),x),x)+2*a*x*diff(y(x),x)+a*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \operatorname {AiryAi}\left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+c_{2} \operatorname {AiryBi}\left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+c_{3} \operatorname {AiryAi}\left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right ) \operatorname {AiryBi}\left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )\]