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 = 0.18734 (sec), leaf count = 34
\[\left \{\left \{y(x)\to \frac {c_2 \left (x^2 \text {Ei}(x)-e^x (x+1)\right )}{2 x}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.075 (sec), leaf count = 27
\[\left [y \left (x \right ) = \textit {\_C1} x +\textit {\_C2} \left (\frac {\left (x +1\right ) {\mathrm e}^{x}}{x}+x \expIntegral \left (1, -x \right )\right )\right ]\] 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))
Maple raw output
[y(x) = _C1*x+_C2*(1/x*(x+1)*exp(x)+x*Ei(1,-x))]