Internal problem ID [11419]
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: 2(e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {\theta ^{\prime }+a \theta ={\mathrm e}^{b t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(theta(t),t)=-a*theta(t)+exp(b*t),theta(t), singsol=all)
\[ \theta \left (t \right ) = \left (\frac {{\mathrm e}^{t \left (a +b \right )}}{a +b}+c_{1} \right ) {\mathrm e}^{-a t} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 31
DSolve[theta'[t]==-a*theta[t]+Exp[b*t],theta[t],t,IncludeSingularSolutions -> True]
\[ \theta (t)\to \frac {e^{-a t} \left (e^{t (a+b)}+c_1 (a+b)\right )}{a+b} \]