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 = 0.0198225 (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 = 0.006 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}} \left ( {\it Erf} \left ( {\frac {i}{2}}\sqrt {2} \left ( x-2 \right ) \right ) {\it \_C1}+{\it \_C2} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(x)*(erf(1/2*I*2^(1/2)*(x-2))*_C1+_C2)