ODE
\[ x y''(x)+(1-2 x) y'(x)-(1-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0127374 (sec), leaf count = 17
\[\left \{\left \{y(x)\to e^x \left (c_2 \log (x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 13
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}} \left ( \ln \left ( x \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[-((1 - x)*y[x]) + (1 - 2*x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*(C[1] + C[2]*Log[x])}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(1-2*x)*diff(y(x),x)-(1-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(x)*(ln(x)*_C2+_C1)