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)]