63.8.2 problem 2

Internal problem ID [13127]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 2, Second order linear equations. Section 2.2.4. Applications. Exercises page 99
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 04:53:45 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&=2\\ x^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 31

dsolve([diff(x(t),t$2)+125/1000*diff(x(t),t)+x(t)=0,x(0) = 2, D(x)(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {2 \,{\mathrm e}^{-\frac {t}{16}} \left (\sqrt {255}\, \sin \left (\frac {\sqrt {255}\, t}{16}\right )+255 \cos \left (\frac {\sqrt {255}\, t}{16}\right )\right )}{255} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 47

DSolve[{D[x[t],{t,2}]+125/1000*D[x[t],t]+x[t]==0,{x[0]==2,Derivative[1][x][0 ]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {2}{255} e^{-t/16} \left (\sqrt {255} \sin \left (\frac {\sqrt {255} t}{16}\right )+255 \cos \left (\frac {\sqrt {255} t}{16}\right )\right ) \]