44.2.25 problem 25

Internal problem ID [6957]
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 : 25
Date solved : Monday, January 27, 2025 at 02:38:29 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.227 (sec). Leaf size: 33

dsolve([diff(y(x),x)=sqrt(y(x)^2-9),y(1) = 4],y(x), singsol=all)
 

\[ y = -\frac {\left (\left (-4-\sqrt {7}\right ) {\mathrm e}^{2 x}+{\mathrm e}^{2} \left (\sqrt {7}-4\right )\right ) {\mathrm e}^{-x -1}}{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 40

DSolve[{D[y[x],x]==Sqrt[y[x]^2-9],{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (4+\sqrt {7}\right ) e^{x-1}-\frac {1}{2} \left (\sqrt {7}-4\right ) e^{1-x} \]