Internal problem ID [11424]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {N^{\prime }-N=-9 \,{\mathrm e}^{-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(N(t),t)=N(t)-9*exp(-t),N(t), singsol=all)
\[ N \left (t \right ) = \left (\frac {9 \,{\mathrm e}^{-2 t}}{2}+c_{1} \right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 32
DSolve[n'[t]==n[t]-9*exp[-t],n[t],t,IncludeSingularSolutions -> True]
\[ n(t)\to e^t \left (\int _1^t-9 e^{-K[1]} \exp (-K[1])dK[1]+c_1\right ) \]