2.10.2 problem 16

Internal problem ID [863]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.4, Mechanical Vibrations. Page 337
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:18:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 x^{\prime \prime }+30 x^{\prime }+63 x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2 \\ x^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 17

ode:=3*diff(diff(x(t),t),t)+30*diff(x(t),t)+63*x(t) = 0; 
ic:=[x(0) = 2, D(x)(0) = 2]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -2 \,{\mathrm e}^{-7 t}+4 \,{\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 20

ode=3*D[x[t],{t,2}]+30*D[x[t],t]+63*x[t]==0; 
ic={x[0]==2,Derivative[1][x][0 ]==2}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-7 t} \left (4 e^{4 t}-2\right ) \end{align*}

✓ Sympy. Time used: 0.119 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(63*x(t) + 30*Derivative(x(t), t) + 3*Derivative(x(t), (t, 2)),0) 
ics = {x(0): 2, Subs(Derivative(x(t), t), t, 0): 2} 
dsolve(ode,func=x(t),ics=ics)
 

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