4.7.15 \((1-x) x y'(x)=2 (x y(x)-1)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00563554 (sec), leaf count = 21

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

Maple
cpu = 0.007 (sec), leaf count = 19

\[ \left \{ y \relax (x ) ={\frac {-2\,\ln \relax (x ) +2\,x+{\it \_C1}}{ \left (-1+x \right ) ^{2}}} \right \} \] Mathematica raw input

DSolve[(1 - x)*x*y'[x] == 2*(-1 + x*y[x]),y[x],x]

Mathematica raw output

{{y[x] -> (2*x + C[1] - 2*Log[x])/(-1 + x)^2}}

Maple raw input

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

Maple raw output

y(x) = (-2*ln(x)+2*x+_C1)/(-1+x)^2