ODE
\[ y''(x)+x y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0177762 (sec), leaf count = 28
\[\left \{\left \{y(x)\to c_1 \text {Ai}\left (\sqrt [3]{-1} x\right )+c_2 \text {Bi}\left (\sqrt [3]{-1} x\right )\right \}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 17
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm Ai}\left (-x\right )}+{\it \_C2}\,{{\rm Bi}\left (-x\right )} \right \} \] Mathematica raw input
DSolve[x*y[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> AiryAi[(-1)^(1/3)*x]*C[1] + AiryBi[(-1)^(1/3)*x]*C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*AiryAi(-x)+_C2*AiryBi(-x)