ODE
\[ x^2 y''(x)+(1-x) x y'(x)-(1-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0239135 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_1 x-\frac {c_2 \left (e^x (x+1)-x^2 \text {Ei}(x)\right )}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.06 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\frac {{\it Ei} \left ( 1,-x \right ) {\it \_C2}\,{x}^{2}+{\it \_C2}\, \left ( 1+x \right ) {{\rm e}^{x}}+{\it \_C1}\,{x}^{2}}{x}} \right \} \] Mathematica raw input
DSolve[-((1 - x)*y[x]) + (1 - x)*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*C[1] - (C[2]*(E^x*(1 + x) - x^2*ExpIntegralEi[x]))/(2*x)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*(1-x)*diff(y(x),x)-(1-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (Ei(1,-x)*_C2*x^2+_C2*(1+x)*exp(x)+_C1*x^2)/x