Internal problem ID [484]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 6.
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: 0.0 (sec). Leaf size: 9
dsolve(x*diff(y(x),x) = (1-y(x)^2)^(1/2),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\ln \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 29
DSolve[x*y'[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*}