80.1.1 problem 2

Internal problem ID [21119]
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 : 2
Date solved : Thursday, October 02, 2025 at 07:08:37 PM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }+\ln \left (3\right ) x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=diff(x(t),t)+ln(3)*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 3^{-t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 18

ode=D[x[t],t]+Log[3]*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 3^{-t}\\ x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.063 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t)*log(3) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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