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 = 0.029353 (sec), leaf count = 46

\[\left \{\left \{y(x)\to c_2 \sin \left (2 \log \left (\sqrt {x-1}+\sqrt {x}\right )\right )+c_1 \cos \left (2 \log \left (\sqrt {x-1}+\sqrt {x}\right )\right )\right \}\right \}\]

Maple ✓
cpu = 0.039 (sec), leaf count = 69

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {1\sqrt {x \left ( -1+x \right ) }\ln \left ( x-{\frac {1}{2}}+\sqrt {{x}^{2}-x} \right ) {\frac {1}{\sqrt {x}}}{\frac {1}{\sqrt {-1+x}}}} \right ) +{\it \_C2}\,\cos \left ( {1\sqrt {x \left ( -1+x \right ) }\ln \left ( x-{\frac {1}{2}}+\sqrt {{x}^{2}-x} \right ) {\frac {1}{\sqrt {x}}}{\frac {1}{\sqrt {-1+x}}}} \right ) \right \} \] 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]*Cos[2*Log[Sqrt[-1 + x] + Sqrt[x]]] + C[2]*Sin[2*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)-2*y(x) = 0, y(x),'implicit')

Maple raw output

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