8.10.6 problem 20

Internal problem ID [867]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 20
Date solved : Wednesday, February 05, 2025 at 04:34:47 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 x^{\prime \prime }+16 x^{\prime }+40 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=5\\ x^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 22

dsolve([2*diff(x(t),t$2)+16*diff(x(t),t)+40*x(t)=0,x(0) = 5, D(x)(0) = 4],x(t), singsol=all)
 

\[ x \left (t \right ) = {\mathrm e}^{-4 t} \left (12 \sin \left (2 t \right )+5 \cos \left (2 t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

DSolve[{2*D[x[t],{t,2}]+16*D[x[t],t]+40*x[t]==0,{x[0]==5,Derivative[1][x][0 ]==4}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-4 t} (12 \sin (2 t)+5 \cos (2 t)) \]