74.20.5 problem 5

Internal problem ID [16637]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 5. Applications of Higher Order Equations. Exercises 5.2, page 241
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 09:13:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+4 x^{\prime }+13 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1\\ x^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 21

dsolve([diff(x(t),t$2)+4*diff(x(t),t)+13*x(t)=0,x(0) = 1, D(x)(0) = -1],x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 25

DSolve[{D[x[t],{t,2}]+4*D[x[t],t]+13*x[t]==0,{x[0]==1,Derivative[1][x][0 ]==-1}},x[t],t,IncludeSingularSolutions -> True]
 

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