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