63.5.11 problem 2(e)

Internal problem ID [13085]
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)
Date solved : Tuesday, January 28, 2025 at 04:51:49 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} \theta ^{\prime }&=-a \theta +{\mathrm e}^{b t} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

dsolve(diff(theta(t),t)=-a*theta(t)+exp(b*t),theta(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 31

DSolve[D[ theta[t],t]==-a*theta[t]+Exp[b*t],theta[t],t,IncludeSingularSolutions -> True]
 

\[ \theta (t)\to \frac {e^{-a t} \left (e^{t (a+b)}+c_1 (a+b)\right )}{a+b} \]