10.2.6 problem 6

Internal problem ID [1134]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 6
Date solved : Monday, January 27, 2025 at 04:35:13 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

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

\[ y = \sin \left (\ln \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 29

DSolve[x*D[y[x],x] == (1-y[x]^2)^(1/2),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*}