47.1.18 problem 18

Internal problem ID [7399]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:52:25 PM
CAS classification : [_separable]

\begin{align*} \frac {1}{\sqrt {-x^{2}+1}}+\frac {y^{\prime }}{\sqrt {1-y^{2}}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

dsolve(1/sqrt(1-x^2)+diff(y(x),x)/sqrt(1-y(x)^2)=0,y(x), singsol=all)
 

\[ y = -\sin \left (\arcsin \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.201 (sec). Leaf size: 23

DSolve[1/Sqrt[1-x^2]+D[y[x],x]/Sqrt[1-y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sin (\arcsin (x)-c_1) \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}