ODE
\[ y''(x)-x y'(x)-((1-x) y(x))=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.183232 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \sqrt {\frac {\pi }{2}} c_2 e^{x-2} \text {erfi}\left (\frac {x-2}{\sqrt {2}}\right )+c_1 e^x\right \}\right \}\]
Maple ✓
cpu = 0.053 (sec), leaf count = 28
\[\left [y \left (x \right ) = \erf \left (\frac {i \sqrt {2}\, x}{2}-i \sqrt {2}\right ) {\mathrm e}^{x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{x}\right ]\] Mathematica raw input
DSolve[-((1 - x)*y[x]) - x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] + E^(-2 + x)*Sqrt[Pi/2]*C[2]*Erfi[(-2 + x)/Sqrt[2]]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-x*diff(y(x),x)-(1-x)*y(x) = 0, y(x))
Maple raw output
[y(x) = erf(1/2*I*2^(1/2)*x-I*2^(1/2))*exp(x)*_C1+_C2*exp(x)]