44.1.44 problem 46

Internal problem ID [6919]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 46
Date solved : Monday, January 27, 2025 at 02:35:04 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=9-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 31

dsolve(diff(y(x),x)^2=9-y(x)^2,y(x), singsol=all)
 

\begin{align*} y &= -3 \\ y &= 3 \\ y &= -3 \sin \left (-x +c_{1} \right ) \\ y &= 3 \sin \left (-x +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.119 (sec). Leaf size: 107

DSolve[D[y[x],x]^2==9-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {3 \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} \\ y(x)\to \frac {3 \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} \\ y(x)\to -\frac {3 \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to \frac {3 \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to -3 \\ y(x)\to 3 \\ \end{align*}