74.22.14 problem 14

Internal problem ID [16582]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 6. Systems of Differential Equations. Exercises 6.1, page 282
Problem number : 14
Date solved : Thursday, March 13, 2025 at 08:23:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+6 x^{\prime }+9 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(x(t),t),t)+6*diff(x(t),t)+9*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x \left (t \right ) = {\mathrm e}^{-3 t} \left (c_{2} t +c_{1} \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[x[t],{t,2}]+6*D[x[t],t]+9*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\[ x(t)\to e^{-3 t} (c_2 t+c_1) \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(9*x(t) + 6*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (C_{1} + C_{2} t\right ) e^{- 3 t} \]