7.8.1 problem 1

Internal problem ID [215]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:42:24 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5 \end{align*}

✓ Solution by Maple

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

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

\[ y = -\frac {5 \,{\mathrm e}^{-x}}{2}+\frac {5 \,{\mathrm e}^{x}}{2} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 21

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

\[ y(x)\to \frac {5}{2} e^{-x} \left (e^{2 x}-1\right ) \]