80.1.5 problem 6

Internal problem ID [21123]
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 : 6
Date solved : Thursday, October 02, 2025 at 07:09:20 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 8

ode:=diff(x(t),t) = k*x(t); 
ic:=[x(0) = 1]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = {\mathrm e}^{k t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 10

ode=D[x[t],t]==k*x[t]; 
ic={x[0]==1}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{k t} \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
k = symbols("k") 
x = Function("x") 
ode = Eq(-k*x(t) + Derivative(x(t), t),0) 
ics = {x(0): 1} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = e^{k t} \]