80.5.14 problem B 14

Internal problem ID [21235]
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 14
Date solved : Thursday, October 02, 2025 at 07:27:09 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ x = c_1 +c_2 \,{\mathrm e}^{-p t} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 21

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

\begin{align*} x(t)&\to c_2-\frac {c_1 e^{-p t}}{p} \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 10

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

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