16.1.11 problem 3(e)

Internal problem ID [3413]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(e)
Date solved : Monday, January 27, 2025 at 07:36:03 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 29

DSolve[D[y[x],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*}