2.10.3 problem 17

Internal problem ID [864]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 04:18:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+8 x^{\prime }+16 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=5 \\ x^{\prime }\left (0\right )&=-10 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 14

ode:=diff(diff(x(t),t),t)+8*diff(x(t),t)+16*x(t) = 0; 
ic:=[x(0) = 5, D(x)(0) = -10]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 17

ode=D[x[t],{t,2}]+8*D[x[t],t]+16*x[t]==0; 
ic={x[0]==5,Derivative[1][x][0 ]==-10}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 5 e^{-4 t} (2 t+1) \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(16*x(t) + 8*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {x(0): 5, Subs(Derivative(x(t), t), t, 0): -10} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (10 t + 5\right ) e^{- 4 t} \]