2.10.7 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 : Tuesday, September 30, 2025 at 04:18:49 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*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 23

ode:=diff(diff(x(t),t),t)+10*diff(x(t),t)+125*x(t) = 0; 
ic:=[x(0) = 6, D(x)(0) = 50]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

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

\begin{align*} x(t)&\to e^{-5 t} (8 \sin (10 t)+6 \cos (10 t)) \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(125*x(t) + 10*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 6, Subs(Derivative(x(t), t), t, 0): 50} 
dsolve(ode,func=x(t),ics=ics)
 

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