ODE
\[ y''(x)-y'(x)+x y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0157907 (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 = 0.056 (sec), leaf count = 26
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {x}{2}}}} \left ( {{\rm Bi}\left ({\frac {1}{4}}-x\right )}{\it \_C2}+{{\rm Ai}\left ({\frac {1}{4}}-x\right )}{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(1/2*x)*(AiryBi(1/4-x)*_C2+AiryAi(1/4-x)*_C1)