4.8.25 \(\left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right )\)

ODE
\[ \left (1-x^4\right ) y'(x)=2 x \left (1-y(x)^2\right ) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.032486 (sec), leaf count = 45

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

Maple
cpu = 0.022 (sec), leaf count = 28

\[ \left \{ {\it \_C1}+{\frac {\ln \left (-1+x \right ) }{2}}+{\frac {\ln \left (1+x \right ) }{2}}-{\frac {\ln \left ({x}^{2}+1 \right ) }{2}}+{\it Artanh} \left (y \relax (x ) \right ) =0 \right \} \] Mathematica raw input

DSolve[(1 - x^4)*y'[x] == 2*x*(1 - y[x]^2),y[x],x]

Mathematica raw output

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

Maple raw input

dsolve((-x^4+1)*diff(y(x),x) = 2*x*(1-y(x)^2), y(x),'implicit')

Maple raw output

_C1+1/2*ln(-1+x)+1/2*ln(1+x)-1/2*ln(x^2+1)+arctanh(y(x)) = 0