ODE
\[ x (2-x)^2 y''(x)+2 (2-x) y'(x)+2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.168395 (sec), leaf count = 32
\[\left \{\left \{y(x)\to -\frac {1}{2} (x-2) (-c_2 \log (2-x)+c_2 \log (x)+2 c_1)\right \}\right \}\]
Maple ✓
cpu = 0.058 (sec), leaf count = 24
\[[y \left (x \right ) = \textit {\_C1} \left (x -2\right )+\textit {\_C2} \left (x -2\right ) \left (\ln \left (x \right )-\ln \left (x -2\right )\right )]\] Mathematica raw input
DSolve[2*y[x] + 2*(2 - x)*y'[x] + (2 - x)^2*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*((-2 + x)*(2*C[1] - C[2]*Log[2 - x] + C[2]*Log[x]))}}
Maple raw input
dsolve(x*(2-x)^2*diff(diff(y(x),x),x)+2*(2-x)*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-2)+_C2*(x-2)*(ln(x)-ln(x-2))]