63.5.24 problem 9

Internal problem ID [13027]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 9
Date solved : Monday, March 31, 2025 at 07:31:23 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=a x+b \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(x(t),t) = a*x(t)+b; 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {b}{a}+{\mathrm e}^{a t} c_1 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 30

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

\begin{align*} x(t)\to -\frac {b}{a}+c_1 e^{a t} \\ x(t)\to -\frac {b}{a} \\ \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 12

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

\[ x{\left (t \right )} = C_{1} e^{a t} - \frac {b}{a} \]