63.5.16 problem 3(d)

Internal problem ID [13090]
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 : 3(d)
Date solved : Tuesday, January 28, 2025 at 04:51:58 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} N^{\prime }&=N-9 \,{\mathrm e}^{-t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(N(t),t)=N(t)-9*exp(-t),N(t), singsol=all)
 

\[ N = \frac {9 \,{\mathrm e}^{-t}}{2}+c_{1} {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 32

DSolve[D[ n[t],t]==n[t]-9*exp[-t],n[t],t,IncludeSingularSolutions -> True]
 

\[ n(t)\to e^t \left (\int _1^t-9 e^{-K[1]} \exp (-K[1])dK[1]+c_1\right ) \]