73.11.11 problem 17.2 (e)

Internal problem ID [15325]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.2 (e)
Date solved : Tuesday, January 28, 2025 at 07:52:37 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-9 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: 0.016 (sec). Leaf size: 17

dsolve([diff(y(x),x$2)-9*y(x)=0,y(0) = 0, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{-3 x}}{6}+\frac {{\mathrm e}^{3 x}}{6} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[{D[y[x],{x,2}]-9*y[x]==0,{y[0]==0,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-3 x} \left (e^{6 x}-1\right ) \]