4.25.7 $y^{″}(x)+xy(x)=0$

ODE
$$y^{″}(x)+xy(x)=0$$ ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0177762 (sec), leaf count = 28

$$\left\{\{y(x)\to c_1\text{Ai}\left(\sqrt[3]{-1}x\right)+c_2\text{Bi}\left(\sqrt[3]{-1}x\right)\}\right\}$$

Maple ✓
cpu = 0.043 (sec), leaf count = 17

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\mathrm{A}\mathrm{i}(-x)+\mathit{\_}\mathit{C}\mathit{2}\mathrm{B}\mathrm{i}(-x)\}$$ 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)