71.9.11 problem 13

Internal problem ID [14490]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 06:42:23 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 )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

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

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

✓ 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] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

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