ODE
\[ y'''(x)+2 a x y'(x)+a y(x)=0 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.160392 (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 = 0.087 (sec), leaf count = 55
\[\left [y \left (x \right ) = \textit {\_C1} \AiryAi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+\textit {\_C2} \AiryBi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )^{2}+\textit {\_C3} \AiryAi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right ) \AiryBi \left (-\frac {2^{\frac {2}{3}} a^{\frac {1}{3}} x}{2}\right )\right ]\] Mathematica raw input
DSolve[a*y[x] + 2*a*x*y'[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> AiryAi[(-1/2)^(1/3)*a^(1/3)*x]^2*C[1] + AiryAi[(-1/2)^(1/3)*a^(1/3)*x]*AiryBi[(-1/2)^(1/3)*a^(1/3)*x]*C[2] + AiryBi[(-1/2)^(1/3)*a^(1/3)*x]^2*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+2*a*x*diff(y(x),x)+a*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*AiryAi(-1/2*2^(2/3)*a^(1/3)*x)^2+_C2*AiryBi(-1/2*2^(2/3)*a^(1/3)*x)^2+_C3*AiryAi(-1/2*2^(2/3)*a^(1/3)*x)*AiryBi(-1/2*2^(2/3)*a^(1/3)*x)]