ODE
\[ \left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x) \] ODE Classification
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.29351 (sec), leaf count = 47
\[\left \{\left \{y(x)\to \frac {x \log (1-x)-x \log (x+1)+2 c_1 x+2}{\log (1-x)-\log (x+1)+2 c_1}\right \}\right \}\]
Maple ✓
cpu = 0.146 (sec), leaf count = 14
\[\left [y \left (x \right ) = x +\frac {1}{-\arctanh \left (x \right )+\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[(1 - x^2)*y'[x] == 1 - (2*x - y[x])*y[x],y[x],x]
Mathematica raw output
{{y[x] -> (2 + 2*x*C[1] + x*Log[1 - x] - x*Log[1 + x])/(2*C[1] + Log[1 - x] - Log[1 + x])}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x) = 1-(2*x-y(x))*y(x), y(x))
Maple raw output
[y(x) = x+1/(-arctanh(x)+_C1)]