44.5.18 problem 18

Internal problem ID [7080]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:47:20 PM
CAS classification : [_separable]

\begin{align*} n^{\prime }+n&=n t \,{\mathrm e}^{t +2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(diff(n(t),t)+n(t)=n(t)*t*exp(t+2),n(t), singsol=all)
 

\[ n = c_{1} {\mathrm e}^{\left (t -1\right ) {\mathrm e}^{t +2}-t} \]

✓ Solution by Mathematica

Time used: 0.087 (sec). Leaf size: 28

DSolve[D[n[t],t]+n[t]==n[t]*t*Exp[t+2],n[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} n(t)\to c_1 e^{e^{t+2} (t-1)-t} \\ n(t)\to 0 \\ \end{align*}