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 = 0.0135751 (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 = 0.037 (sec), leaf count = 55
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {{\rm Ai}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )} \right ) ^{2}+{\it \_C2}\, \left ( {{\rm Bi}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )} \right ) ^{2}+{\it \_C3}\,{{\rm Ai}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )}{{\rm Bi}\left (-{\frac {{2}^{{\frac {2}{3}}}x}{2}\sqrt [3]{a}}\right )} \right \} \] 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),'implicit')
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)