Internal problem ID [1933]
Book: Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section: Exercis 2, page 5
Problem number: 3(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -\sqrt {1-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 9
dsolve(diff(y(x),x)*x=sqrt(1-y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\ln \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 1.833 (sec). Leaf size: 58
DSolve[y'[x]*x==Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\tan (\log (x)+c_1)}{\sqrt {\sec ^2(\log (x)+c_1)}} \\ y(x)\to \frac {\tan (\log (x)+c_1)}{\sqrt {\sec ^2(\log (x)+c_1)}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}