ODE No. 1454

\[ 2 a x y'(x)+a y(x)+y^{(3)}(x)=0 \] Mathematica : cpu = 0.0062971 (sec), leaf count = 79

DSolve[a*y[x] + 2*a*x*Derivative[1][y][x] + Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \text {Ai}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )^2+c_3 \text {Bi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )^2+c_2 \text {Ai}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right ) \text {Bi}\left (\sqrt [3]{-\frac {1}{2}} \sqrt [3]{a} x\right )\right \}\right \}\] Maple : cpu = 0.053 (sec), leaf count = 55

dsolve(diff(diff(diff(y(x),x),x),x)+2*a*x*diff(y(x),x)+a*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \AiryAi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+c_{2} \AiryBi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+c_{3} \AiryAi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right ) \AiryBi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )\]