80.5.24 problem B 24

Internal problem ID [21245]
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 24
Date solved : Friday, October 03, 2025 at 07:49:25 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+2 x^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.046 (sec). Leaf size: 15

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

\[ x = \operatorname {signum}\left (a \sinh \left (t \right ) {\mathrm e}^{-t}\right ) \infty \]

✗ Mathematica

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

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✓ Sympy. Time used: 0.085 (sec). Leaf size: 10

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

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