ODE
\[ 2 (1-x) x y''(x)+(1-2 x) y'(x)+8 y(x)=0 \] ODE Classification
[_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0804615 (sec), leaf count = 49
\[\left \{\left \{y(x)\to c_1 \cosh \left (4 \log \left (\sqrt {x-1}+\sqrt {x}\right )\right )+i c_2 \sinh \left (4 \log \left (\sqrt {x-1}+\sqrt {x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( 8\,{x}^{2}-8\,x+1 \right ) +{\it \_C2}\, \left ( -1+2\,x \right ) \sqrt {x \left ( -1+x \right ) } \right \} \] Mathematica raw input
DSolve[8*y[x] + (1 - 2*x)*y'[x] + 2*(1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cosh[4*Log[Sqrt[-1 + x] + Sqrt[x]]] + I*C[2]*Sinh[4*Log[Sqrt[-1 + x] + Sqrt[x]]]}}
Maple raw input
dsolve(2*x*(1-x)*diff(diff(y(x),x),x)+(1-2*x)*diff(y(x),x)+8*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*(8*x^2-8*x+1)+_C2*(-1+2*x)*(x*(-1+x))^(1/2)