Internal problem ID [10354]
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 1.3.1 Separable equations. Exercises page
26
Problem number: 1(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-a x-b=0} \]
✓ Solution by Maple
Time used: 0.015 (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: 0.037 (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*}