ODE
\[ (2-x) x y''(x)+2 (1-x) y'(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163143 (sec), leaf count = 37
\[\left \{\left \{y(x)\to c_1 (x-1)-\frac {1}{2} c_2 ((x-1) \log (2-x)-x \log (x)+\log (x)+2)\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 32
\[\left [y \left (x \right ) = \textit {\_C1} \left (x -1\right )+\textit {\_C2} \left (\frac {\left (1-x \right ) \ln \left (x -2\right )}{2}-1+\frac {\left (x -1\right ) \ln \left (x \right )}{2}\right )\right ]\] Mathematica raw input
DSolve[2*y[x] + 2*(1 - x)*y'[x] + (2 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (-1 + x)*C[1] - (C[2]*(2 + (-1 + x)*Log[2 - x] + Log[x] - x*Log[x]))/2}}
Maple raw input
dsolve(x*(2-x)*diff(diff(y(x),x),x)+2*(1-x)*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-1)+_C2*(1/2*(1-x)*ln(x-2)-1+1/2*(x-1)*ln(x))]