Internal problem ID [215]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.4, Mechanical Vibrations. Page 337
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {2 x^{\prime \prime }+12 x^{\prime }+50 x=0} \end {gather*} With initial conditions \begin {align*} [x \relax (0) = 0, x^{\prime }\relax (0) = -8] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([2*diff(x(t),t$2)+12*diff(x(t),t)+50*x(t)=0,x(0) = 0, D(x)(0) = -8],x(t), singsol=all)
\[ x \relax (t ) = -2 \,{\mathrm e}^{-3 t} \sin \left (4 t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{2*x''[t]+12*x'[t]+50*x[t]==0,{x[0]==0,x'[0]==-8}},x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -2 e^{-3 t} \sin (4 t) \\ \end{align*}