4.9.5 \(\sqrt {1-x^4} y'(x)=\sqrt {1-y(x)^4}\)

ODE
\[ \sqrt {1-x^4} y'(x)=\sqrt {1-y(x)^4} \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0508674 (sec), leaf count = 14

\[\left \{\left \{y(x)\to \text {sn}\left (\left .c_1+F\left (\left .\sin ^{-1}(x)\right |-1\right )\right |-1\right )\right \}\right \}\]

Maple
cpu = 0.013 (sec), leaf count = 32

\[ \left \{ \int \!{\frac {1}{\sqrt {-{x}^{4}+1}}}\,{\rm d}x-\int ^{y \relax (x ) }\!{\frac {1}{\sqrt {-{{\it \_a}}^{4}+1}}}{d{\it \_a}}+{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[Sqrt[1 - x^4]*y'[x] == Sqrt[1 - y[x]^4],y[x],x]

Mathematica raw output

{{y[x] -> JacobiSN[C[1] + EllipticF[ArcSin[x], -1], -1]}}

Maple raw input

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

Maple raw output

Int(1/(-x^4+1)^(1/2),x)-Intat(1/(-_a^4+1)^(1/2),_a = y(x))+_C1 = 0