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 = 0.012954 (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 = 0.052 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) =-{\frac {{\it \_C2}\, \left ( -1+x \right ) \ln \left ( x-2 \right ) }{2}}+{\frac {{\it \_C2}\, \left ( -1+x \right ) \ln \left ( x \right ) }{2}}+{\it \_C1}\,x-{\it \_C1}-{\it \_C2} \right \} \] 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),'implicit')
Maple raw output
y(x) = -1/2*_C2*(-1+x)*ln(x-2)+1/2*_C2*(-1+x)*ln(x)+_C1*x-_C1-_C2