80.1.19 problem 16 (b)

Internal problem ID [21137]
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 : 16 (b)
Date solved : Thursday, October 02, 2025 at 07:09:46 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 9

ode:=diff(x(t),t)+x(t) = 4*t; 
ic:=[x(1) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = 4 t -4 \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 10

ode=D[x[t],t]+x[t]==4*t; 
ic={x[1]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.072 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-4*t - x(t) + Derivative(x(t), t),0) 
ics = {x(1): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = - 4 t + \frac {8 e^{t}}{e} - 4 \]