44.2.11 problem 11

Internal problem ID [6943]
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 : 11
Date solved : Monday, January 27, 2025 at 02:37:45 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 15

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

\[ y = -\frac {{\mathrm e}^{-x}}{2}+\frac {3 \,{\mathrm e}^{x}}{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 22

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

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