Internal problem ID [7648]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 67.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(x),x) - sqrt(1-y(x)^4)/sqrt(1-x^4)=0,y(x), singsol=all)
\[ \int \frac {1}{\sqrt {-x^{4}+1}}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\sqrt {-\textit {\_a}^{4}+1}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 40.608 (sec). Leaf size: 38
DSolve[y'[x] - Sqrt[1-y[x]^4]/Sqrt[1-x^4]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {sn}(c_1+\text {EllipticF}(\text {ArcSin}(x),-1)|-1) \\ y(x)\to -1 \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to 1 \\ \end{align*}