29.14.21 problem 402

Internal problem ID [5000]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 402
Date solved : Monday, January 27, 2025 at 10:02:31 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

dsolve(diff(y(x),x)*sqrt(-x^4+1) = sqrt(1-y(x)^4),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 38

DSolve[D[y[x],x] Sqrt[1-x^4]==Sqrt[1-y[x]^4],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {sn}(c_1+\operatorname {EllipticF}(\arcsin (x),-1)|-1) \\ y(x)\to -1 \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to 1 \\ \end{align*}