Internal problem ID [216]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.4, Mechanical Vibrations. Page 337
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {4 x^{\prime \prime }+20 x^{\prime }+169 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 4, x^{\prime }\relax (0) = 16] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ x \relax (t ) = \frac {{\mathrm e}^{-\frac {5 t}{2}} \left (13 \sin \left (6 t \right )+12 \cos \left (6 t \right )\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 29
DSolve[{4*x''[t]+20*x'[t]+169*x[t]==0,{x[0]==4,x'[0]==16}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-5 t/2} (13 \sin (6 t)+12 \cos (6 t)) \\ \end{align*}