Internal problem ID [11432]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-a x=b} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(x(t),t)=a*x(t)+b,x(t), singsol=all)
\[ x \left (t \right ) = -\frac {b}{a}+{\mathrm e}^{a t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 30
DSolve[x'[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*}