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

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

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0275774 (sec), leaf count = 37

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

Maple
cpu = 0.006 (sec), leaf count = 12

\[ \left \{ -{\it Artanh} \relax (x ) +{\it Artanh} \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

-arctanh(x)+arctanh(y(x))+_C1 = 0