Internal problem ID [7128]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 83.
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)
\[ y \left (x \right ) = \sin \left (x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.228 (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*}