8.10.5 problem 19

Internal problem ID [866]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 19
Date solved : Wednesday, February 05, 2025 at 04:34:44 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 x^{\prime \prime }+20 x^{\prime }+169 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=4\\ x^{\prime }\left (0\right )&=16 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 23

dsolve([4*diff(x(t),t$2)+20*diff(x(t),t)+169*x(t)=0,x(0) = 4, D(x)(0) = 16],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {{\mathrm e}^{-\frac {5 t}{2}} \left (13 \sin \left (6 t \right )+12 \cos \left (6 t \right )\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

DSolve[{4*D[x[t],{t,2}]+20*D[x[t],t]+169*x[t]==0,{x[0]==4,Derivative[1][x][0 ]==16}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{3} e^{-5 t/2} (13 \sin (6 t)+12 \cos (6 t)) \]