Internal problem ID [3148]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 402.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {1-x^{4}}-\sqrt {1-y^{4}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x)*sqrt(-x^4+1) = sqrt(1-y(x)^4),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: 40.387 (sec). Leaf size: 38
DSolve[y'[x] Sqrt[1-x^4]==Sqrt[1-y[x]^4],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {sn}(c_1+F(\text {ArcSin}(x)|-1)|-1) \\ y(x)\to -1 \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to 1 \\ \end{align*}