44.2.13 problem 13

Internal problem ID [6945]
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 : 13
Date solved : Monday, January 27, 2025 at 02:37:51 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=5\\ y^{\prime }\left (-1\right )&=-5 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 12

dsolve([diff(y(x),x$2)-y(x)=0,y(-1) = 5, D(y)(-1) = -5],y(x), singsol=all)
 

\[ y = 5 \,{\mathrm e}^{-x -1} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 14

DSolve[{D[y[x],{x,2}]-y[x]==0,{y[-1]==5,Derivative[1][y][-1] == -5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 e^{-x-1} \]