##### 4.25.34 $$y''(x)-y'(x)+x y(x)=0$$

ODE
$y''(x)-y'(x)+x y(x)=0$ ODE Classiﬁcation

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.159258 (sec), leaf count = 50

$\left \{\left \{y(x)\to e^{x/2} \left (c_1 \text {Ai}\left (\frac {1}{4} \sqrt [3]{-1} (4 x-1)\right )+c_2 \text {Bi}\left (\frac {1}{4} \sqrt [3]{-1} (4 x-1)\right )\right )\right \}\right \}$

Maple
cpu = 0.095 (sec), leaf count = 29

$\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\frac {x}{2}} \AiryAi \left (\frac {1}{4}-x \right )+\textit {\_C2} \,{\mathrm e}^{\frac {x}{2}} \AiryBi \left (\frac {1}{4}-x \right )\right ]$ Mathematica raw input

DSolve[x*y[x] - y'[x] + y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> E^(x/2)*(AiryAi[((-1)^(1/3)*(-1 + 4*x))/4]*C[1] + AiryBi[((-1)^(1/3)*(
-1 + 4*x))/4]*C[2])}}

Maple raw input

dsolve(diff(diff(y(x),x),x)-diff(y(x),x)+x*y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*exp(1/2*x)*AiryAi(1/4-x)+_C2*exp(1/2*x)*AiryBi(1/4-x)]