44.5.70 problem 59

Internal problem ID [7132]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 59
Date solved : Tuesday, February 04, 2025 at 12:29:42 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.044 (sec). Leaf size: 29

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

\begin{align*} y &= -1 \\ y &= 1 \\ y &= -\sin \left (c_1 -x \right ) \\ y &= \sin \left (c_1 -x \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 41

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