2.67   ODE No. 67

\[ y'(x)-\frac {\sqrt {1-y(x)^4}}{\sqrt {1-x^4}}=0 \]

✓ Mathematica : cpu = 0.143761 (sec), leaf count = 14

DSolve[-(Sqrt[1 - y[x]^4]/Sqrt[1 - x^4]) + Derivative[1][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.042 (sec), leaf count = 51

dsolve(diff(y(x),x)-(1-y(x)^4)^(1/2)/(-x^4+1)^(1/2) = 0,y(x))
 

\[\frac {\sqrt {-x^{2}+1}\, \sqrt {x^{2}+1}\, \operatorname {EllipticF}\left (x , i\right )}{\sqrt {-x^{4}+1}}-\left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-\textit {\_a}^{4}+1}}d \textit {\_a} \right )+c_{1} = 0\]