15.19.15 problem 15

Internal problem ID [3299]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:31:45 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 29

dsolve(diff(y(x),x)^2+y(x)^2=1,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: 0.092 (sec). Leaf size: 41

DSolve[D[y[x],x]^2+y[x]^2==1,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*}