80.10.1 problem 24

Internal problem ID [21396]
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 11. Laplace transform. Excercise 11.7 at page 248
Problem number : 24
Date solved : Thursday, October 02, 2025 at 07:30:47 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+x&={\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.051 (sec). Leaf size: 6

ode:=diff(x(t),t)+x(t) = exp(t); 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t),method='laplace');
 

\[ x = \sinh \left (t \right ) \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 21

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

\begin{align*} x(t)&\to \frac {1}{2} e^{-t} \left (e^{2 t}-1\right ) \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 14

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

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