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 = 0.0318517 (sec), leaf count = 39
\[\left \{\left \{y(x)\to c_1 \cosh (\log (1-x)-\log (x))+i c_2 \sinh (\log (1-x)-\log (x))\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sinh \left ( -\ln \left ( -1+x \right ) +\ln \left ( x \right ) \right ) +{\it \_C2}\,\cosh \left ( -\ln \left ( -1+x \right ) +\ln \left ( x \right ) \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*sinh(-ln(-1+x)+ln(x))+_C2*cosh(-ln(-1+x)+ln(x))