Internal problem ID [4964]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x y^{\prime }-\sqrt {1-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 9
dsolve(x*diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (c_{1}+\ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.333 (sec). Leaf size: 29
DSolve[x*y'[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*}