ODE
\[ x y''(x)-(x+1) y'(x)+2 (1-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.101505 (sec), leaf count = 30
\[\left \{\left \{y(x)\to c_1 e^{2 x}-\frac {1}{9} c_2 e^{-x} (3 x+1)\right \}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{2\,x}}+{\it \_C2}\,{{\rm e}^{-x}} \left ( 1+3\,x \right ) \right \} \] Mathematica raw input
DSolve[2*(1 - x)*y[x] - (1 + x)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(2*x)*C[1] - ((1 + 3*x)*C[2])/(9*E^x)}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(1+x)*diff(y(x),x)+2*(1-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*exp(2*x)+_C2*exp(-x)*(1+3*x)