4.33.13 \(2 (1-x) x y''(x)+(1-2 x) y'(x)-2 y(x)=0\)

ODE
\[ 2 (1-x) x y''(x)+(1-2 x) y'(x)-2 y(x)=0 \] ODE Classification

[_Jacobi, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.178245 (sec), leaf count = 41

\[\left \{\left \{y(x)\to c_1 \cosh \left (2 \sin ^{-1}\left (\sqrt {1-x}\right )\right )-i c_2 \sinh \left (2 \sin ^{-1}\left (\sqrt {1-x}\right )\right )\right \}\right \}\]

Maple ✓
cpu = 0.105 (sec), leaf count = 69

\[\left [y \left (x \right ) = \textit {\_C1} \sin \left (\frac {\sqrt {x \left (x -1\right )}\, \ln \left (-\frac {1}{2}+x +\sqrt {x^{2}-x}\right )}{\sqrt {x}\, \sqrt {x -1}}\right )+\textit {\_C2} \cos \left (\frac {\sqrt {x \left (x -1\right )}\, \ln \left (-\frac {1}{2}+x +\sqrt {x^{2}-x}\right )}{\sqrt {x}\, \sqrt {x -1}}\right )\right ]\] Mathematica raw input

DSolve[-2*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[2*ArcSin[Sqrt[1 - x]]] - I*C[2]*Sinh[2*ArcSin[Sqrt[1 - x]]]}
}

Maple raw input

dsolve(2*x*(1-x)*diff(diff(y(x),x),x)+(1-2*x)*diff(y(x),x)-2*y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*sin((x*(x-1))^(1/2)/x^(1/2)/(x-1)^(1/2)*ln(-1/2+x+(x^2-x)^(1/2)))+_C
2*cos((x*(x-1))^(1/2)/x^(1/2)/(x-1)^(1/2)*ln(-1/2+x+(x^2-x)^(1/2)))]