8.10.7 problem 21

Internal problem ID [868]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 21
Date solved : Wednesday, February 05, 2025 at 04:34:50 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+10 x^{\prime }+125 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=6\\ x^{\prime }\left (0\right )&=50 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 23

dsolve([diff(x(t),t$2)+10*diff(x(t),t)+125*x(t)=0,x(0) = 6, D(x)(0) = 50],x(t), singsol=all)
 

\[ x \left (t \right ) = 2 \,{\mathrm e}^{-5 t} \left (4 \sin \left (10 t \right )+3 \cos \left (10 t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 24

DSolve[{D[x[t],{t,2}]+10*D[x[t],t]+125*x[t]==0,{x[0]==6,Derivative[1][x][0 ]==50}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^{-5 t} (8 \sin (10 t)+6 \cos (10 t)) \]