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 = 0.298886 (sec), leaf count = 37
\[\left \{\left \{y(x)\to -\frac {x+e^{2 c_1} (x-1)+1}{-x+e^{2 c_1} (x-1)-1}\right \}\right \}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 13
\[[y \left (x \right ) = -\tanh \left (-\arctanh \left (x \right )+\textit {\_C1} \right )]\] 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))
Maple raw output
[y(x) = -tanh(-arctanh(x)+_C1)]