76.1.6 problem 6

Internal problem ID [17305]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 09:59:14 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

dsolve(x*diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 29

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

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