73.11.12 problem 17.2 (f)

Internal problem ID [15326]
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 (f)
Date solved : Tuesday, January 28, 2025 at 07:52:41 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 )&=3\\ y^{\prime }\left (0\right )&=-3 \end{align*}

✓ Solution by Maple

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

dsolve([diff(y(x),x$2)-9*y(x)=0,y(0) = 3, D(y)(0) = -3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]-9*y[x]==0,{y[0]==3,Derivative[1][y][0] ==-3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (e^{6 x}+2\right ) \]