44.2.26 problem 26

Internal problem ID [6958]
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. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:38:36 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (5\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 5

dsolve([diff(y(x),x)=sqrt(y(x)^2-9),y(5) = 3],y(x), singsol=all)
 

\[ y = 3 \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 6

DSolve[{D[y[x],x]==Sqrt[y[x]^2-9],{y[5]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 \]