Internal problem ID [217]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.4, Mechanical Vibrations. Page 337
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 x^{\prime \prime }+16 x^{\prime }+40 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 5, x^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.007 (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)
\[ x \relax (t ) = {\mathrm e}^{-4 t} \left (12 \sin \left (2 t \right )+5 \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[{2*x''[t]+16*x'[t]+40*x[t]==0,{x[0]==5,x'[0]==4}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-4 t} (12 \sin (2 t)+5 \cos (2 t)) \\ \end{align*}