80.1.24 problem 28

Internal problem ID [21142]
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 : 28
Date solved : Thursday, October 02, 2025 at 07:09:52 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x^{\prime }+2 x&=6 t \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(x(t),t)+2*x(t) = 6*t; 
dsolve(ode,x(t), singsol=all);
 

\[ x = 3 t -\frac {3}{2}+{\mathrm e}^{-2 t} c_1 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 20

ode=D[x[t],t]+2*x[t]==6*t; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 3 t+c_1 e^{-2 t}-\frac {3}{2} \end{align*}

✓ Sympy. Time used: 0.073 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*t + 2*x(t) + Derivative(x(t), t),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} e^{- 2 t} + 3 t - \frac {3}{2} \]