ODE
\[ 2 (1-x) x y''(x)+(1-x) y'(x)+y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.173155 (sec), leaf count = 34
\[\left \{\left \{y(x)\to c_1 (-x)+c_2 \sqrt {x}-c_2 (x-1) \tanh ^{-1}\left (\sqrt {x}\right )+c_1\right \}\right \}\]
Maple ✓
cpu = 0.148 (sec), leaf count = 40
\[\left [y \left (x \right ) = \textit {\_C1} \left (x -1\right )+\textit {\_C2} \left (\frac {\left (x -1\right ) \ln \left (\sqrt {x}-1\right )}{2}+\frac {\left (1-x \right ) \ln \left (\sqrt {x}+1\right )}{2}+\sqrt {x}\right )\right ]\] Mathematica raw input
DSolve[y[x] + (1 - x)*y'[x] + 2*(1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1] - x*C[1] + Sqrt[x]*C[2] - (-1 + x)*ArcTanh[Sqrt[x]]*C[2]}}
Maple raw input
dsolve(2*x*(1-x)*diff(diff(y(x),x),x)+(1-x)*diff(y(x),x)+y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-1)+_C2*(1/2*(x-1)*ln(x^(1/2)-1)+1/2*(1-x)*ln(x^(1/2)+1)+x^(1/2))]