44.2.12 problem 12

Internal problem ID [6944]
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 : 12
Date solved : Monday, January 27, 2025 at 02:37:48 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 )&=0\\ y^{\prime }\left (1\right )&={\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 17

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

\[ y = -\frac {{\mathrm e}^{-x +2}}{2}+\frac {{\mathrm e}^{x}}{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

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

\[ y(x)\to \frac {e^x}{2}-\frac {e^{2-x}}{2} \]