77.1.6 problem 17 (page 27)

Internal problem ID [17896]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 17 (page 27)
Date solved : Tuesday, January 28, 2025 at 11:10:35 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve(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: 0.189 (sec). Leaf size: 33

DSolve[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 -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}