44.2.27 problem 27

Internal problem ID [6959]
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 : 27
Date solved : Monday, January 27, 2025 at 02:38:40 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\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(2) = -3],y(x), singsol=all)
 

\[ y = -3 \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 25

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

\[ y(x)\to -\frac {3}{2} e^{-x-2} \left (e^{2 x}+e^4\right ) \]