4.6.50 \(\left (1-x^2\right ) y'(x)=1-(2 x-y(x)) y(x)\)

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 = 0.0152203 (sec), leaf count = 47

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

Maple
cpu = 0.107 (sec), leaf count = 14

\[ \left \{ y \relax (x ) =x+ \left ({\it \_C1}-{\it Artanh} \relax (x ) \right ) ^{-1} \right \} \] 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] - Lo
g[1 + x])}}

Maple raw input

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

Maple raw output

y(x) = x+1/(_C1-arctanh(x))