8.10.4 problem 18

Internal problem ID [865]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 18
Date solved : Wednesday, February 05, 2025 at 04:34:41 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 x^{\prime \prime }+12 x^{\prime }+50 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=0\\ x^{\prime }\left (0\right )&=-8 \end{align*}

✓ Solution by Maple

Time used: 0.008 (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)
 

\[ x \left (t \right ) = -2 \,{\mathrm e}^{-3 t} \sin \left (4 t \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 16

DSolve[{2*D[x[t],{t,2}]+12*D[x[t],t]+50*x[t]==0,{x[0]==0,Derivative[1][x][0 ]==-8}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to -2 e^{-3 t} \sin (4 t) \]