29.26.20 problem 756

Internal problem ID [5341]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 756
Date solved : Monday, January 27, 2025 at 11:15:54 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 29

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

\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= 1 \\ y \left (x \right ) &= -\sin \left (-x +c_{1} \right ) \\ y \left (x \right ) &= \sin \left (-x +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 41

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

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