56.1.84 problem 83

Internal problem ID [8796]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 83
Date solved : Monday, January 27, 2025 at 05:00:52 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {1-y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 8

dsolve(diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
 

\[ y = \sin \left (x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 28

DSolve[D[y[x],x]==Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sin (x+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}