Internal problem ID [214]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.4, Mechanical Vibrations. Page 337
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {x^{\prime \prime }+8 x^{\prime }+16 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 5, x^{\prime }\relax (0) = -10] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 14
dsolve([diff(x(t),t$2)+8*diff(x(t),t)+16*x(t)=0,x(0) = 5, D(x)(0) = -10],x(t), singsol=all)
\[ x \relax (t ) = \left (5+10 t \right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 17
DSolve[{x''[t]+8*x'[t]+16*x[t]==0,{x[0]==5,x'[0]==-10}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 5 e^{-4 t} (2 t+1) \\ \end{align*}