8.10.3 problem 17

Internal problem ID [864]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 17
Date solved : Monday, January 27, 2025 at 03:10:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=5\\ x^{\prime }\left (0\right )&=-10 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve([diff(x(t),t$2)+8*diff(x(t),t)+16*x(t)=0,x(0) = 5, D(x)(0) = -10],x(t), singsol=all)
 

\[ x \left (t \right ) = \left (5+10 t \right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 17

DSolve[{D[x[t],{t,2}]+8*D[x[t],t]+16*x[t]==0,{x[0]==5,Derivative[1][x][0 ]==-10}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to 5 e^{-4 t} (2 t+1) \]