4.7.37 \(2 (1-x) x y'(x)+(1-2 x) y(x)+x=0\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.035545 (sec), leaf count = 66

\[\left \{\left \{y(x)\to \frac {2 c_1 \sqrt {-(x-1) x}-x^2+x-\sqrt {x-1} \sqrt {x} \log \left (\sqrt {x-1}+\sqrt {x}\right )}{2 x-2 x^2}\right \}\right \}\]

Maple
cpu = 0.017 (sec), leaf count = 37

\[ \left \{ y \relax (x ) ={\frac {1}{4} \left (2\,\sqrt {x \left (-1+x \right ) }+\ln \left (-{\frac {1}{2}}+x+\sqrt {x \left (-1+x \right ) } \right ) +4\,{\it \_C1} \right ) {\frac {1}{\sqrt {x \left (-1+x \right ) }}}} \right \} \] 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] -> (x - x^2 + 2*Sqrt[-((-1 + x)*x)]*C[1] - Sqrt[-1 + x]*Sqrt[x]*Log[Sqrt[
-1 + x] + Sqrt[x]])/(2*x - 2*x^2)}}

Maple raw input

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

Maple raw output

y(x) = 1/4*(2*(x*(-1+x))^(1/2)+ln(-1/2+x+(x*(-1+x))^(1/2))+4*_C1)/(x*(-1+x))^(1/
2)