60.1.67 problem 67

Internal problem ID [10081]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 67
Date solved : Monday, January 27, 2025 at 06:24:55 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 32

dsolve(diff(y(x),x) - sqrt(1-y(x)^4)/sqrt(1-x^4)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 38

DSolve[D[y[x],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+\operatorname {EllipticF}(\arcsin (x),-1)|-1) \\ y(x)\to -1 \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to 1 \\ \end{align*}