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 = 0.182779 (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 = 0.06 (sec), leaf count = 22
\[[y \left (x \right ) = {\mathrm e}^{2 x} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{-x} \left (1+3 x \right )]\] 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)-(x+1)*diff(y(x),x)+2*(1-x)*y(x) = 0, y(x))
Maple raw output
[y(x) = exp(2*x)*_C1+_C2*exp(-x)*(1+3*x)]