ODE
\[ 2 (1-x) x y''(x)+(1-x) y'(x)+y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0523408 (sec), leaf count = 54
\[\left \{\left \{y(x)\to \frac {1}{2} c_2 \left (2 \sqrt {x}+(x-1) \log \left (1-\sqrt {x}\right )-(x-1) \log \left (\sqrt {x}+1\right )\right )-c_1 (x-1)\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}\, \left ( -1+x \right ) }{2}\ln \left ( \sqrt {x}-1 \right ) }-{\frac {{\it \_C2}\, \left ( -1+x \right ) }{2}\ln \left ( \sqrt {x}+1 \right ) }+\sqrt {x}{\it \_C2}+{\it \_C1}\, \left ( -1+x \right ) \right \} \] 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] -> -((-1 + x)*C[1]) + (C[2]*(2*Sqrt[x] + (-1 + x)*Log[1 - Sqrt[x]] - (-1 + x)*Log[1 + Sqrt[x]]))/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),'implicit')
Maple raw output
y(x) = 1/2*_C2*(-1+x)*ln(x^(1/2)-1)-1/2*ln(x^(1/2)+1)*_C2*(-1+x)+x^(1/2)*_C2+_C1*(-1+x)