ODE
\[ (1-x) x y'(x)=2 (x y(x)-1) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.179541 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \frac {2 x-2 \log (x)+c_1}{(x-1)^2}\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 19
\[\left [y \left (x \right ) = \frac {2 x -2 \ln \left (x \right )+\textit {\_C1}}{\left (x -1\right )^{2}}\right ]\] 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))
Maple raw output
[y(x) = (2*x-2*ln(x)+_C1)/(x-1)^2]