80.5.13 problem B 13

Internal problem ID [21234]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 5. Second order equations. Excercise 5.9 at page 119
Problem number : B 13
Date solved : Thursday, October 02, 2025 at 07:27:09 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+5 x^{\prime }+6 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(diff(x(t),t),t)+5*diff(x(t),t)+6*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \left (c_2 \,{\mathrm e}^{t}+c_1 \right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 20

ode=D[x[t],{t,2}]+5*D[x[t],t]+6*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-3 t} \left (c_2 e^t+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(6*x(t) + 5*Derivative(x(t), t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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