Internal problem ID [10433]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {x^{\prime \prime }+\frac {x^{\prime }}{8}+x=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 2, x^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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: 0.005 (sec). Leaf size: 47
DSolve[{x''[t]+125/1000*x'[t]+x[t]==0,{x[0]==2,x'[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} 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 ) \\ \end{align*}