80.1.2 problem 3

Internal problem ID [21120]
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 1. First order linear differential equations. Excercise 1.5 at page 13
Problem number : 3
Date solved : Thursday, October 02, 2025 at 07:08:38 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }+4 x&=4 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(x(t),t)+4*x(t) = 4; 
dsolve(ode,x(t), singsol=all);
 

\[ x = 1+{\mathrm e}^{-4 t} c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 20

ode=D[x[t],t]+4*x[t]==4; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 1+c_1 e^{-4 t}\\ x(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.068 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(4*x(t) + Derivative(x(t), t) - 4,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{- 4 t} + 1 \]