ODE
\[ (1-x)^2 x^2 y''(x)+(1-2 x) (1-x) x y'(x)-y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.222033 (sec), leaf count = 39
\[\{\{y(x)\to c_1 \cosh (\log (1-x)-\log (x))+i c_2 \sinh (\log (1-x)-\log (x))\}\}\]
Maple ✓
cpu = 0.067 (sec), leaf count = 29
\[[y \left (x \right ) = \textit {\_C1} \sinh \left (\ln \left (x \right )-\ln \left (x -1\right )\right )+\textit {\_C2} \cosh \left (\ln \left (x \right )-\ln \left (x -1\right )\right )]\] Mathematica raw input
DSolve[-y[x] + (1 - 2*x)*(1 - x)*x*y'[x] + (1 - x)^2*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cosh[Log[1 - x] - Log[x]] + I*C[2]*Sinh[Log[1 - x] - Log[x]]}}
Maple raw input
dsolve(x^2*(1-x)^2*diff(diff(y(x),x),x)+x*(1-x)*(1-2*x)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sinh(ln(x)-ln(x-1))+_C2*cosh(ln(x)-ln(x-1))]