Internal problem ID [14939]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 1. Basic concepts and definitions. Exercises page 18
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\sqrt {1-y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve(diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (c_{1} +x \right ) \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 28
DSolve[y'[x]==Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}