ODE
\[ 2 (1-x) x y'(x)+(1-2 x) y(x)+x=0 \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.202925 (sec), leaf count = 44
\[\left \{\left \{y(x)\to \frac {\sqrt {-((x-1) x)}+\sin ^{-1}\left (\sqrt {1-x}\right )+2 c_1}{2 \sqrt {-((x-1) x)}}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {1}{2}+\frac {\ln \left (-\frac {1}{2}+x +\sqrt {x \left (x -1\right )}\right )}{4 \sqrt {x \left (x -1\right )}}+\frac {\textit {\_C1}}{\sqrt {x \left (x -1\right )}}\right ]\] Mathematica raw input
DSolve[x + (1 - 2*x)*y[x] + 2*(1 - x)*x*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (Sqrt[-((-1 + x)*x)] + ArcSin[Sqrt[1 - x]] + 2*C[1])/(2*Sqrt[-((-1 + x)*x)])}}
Maple raw input
dsolve(2*x*(1-x)*diff(y(x),x)+x+(1-2*x)*y(x) = 0, y(x))
Maple raw output
[y(x) = 1/2+1/4/(x*(x-1))^(1/2)*ln(-1/2+x+(x*(x-1))^(1/2))+1/(x*(x-1))^(1/2)*_C1]