63.5.24 problem 9

Internal problem ID [13098]
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 : Tuesday, January 28, 2025 at 04:52:14 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==a*x[t]+b,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*}