44.2.28 problem 28

Internal problem ID [6960]
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 : 28
Date solved : Monday, January 27, 2025 at 02:38:43 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.271 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 46

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

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