44.5.16 problem 16

Internal problem ID [7078]
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 : 16
Date solved : Monday, January 27, 2025 at 02:47:16 PM
CAS classification : [_quadrature]

\begin{align*} q^{\prime }&=k \left (q-70\right ) \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

dsolve(diff(q(t),t)=k*(q(t)-70),q(t), singsol=all)
 

\[ q = 70+{\mathrm e}^{k t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 20

DSolve[D[q[t],t]==k*(q[t]-70),q[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} q(t)\to 70+c_1 e^{k t} \\ q(t)\to 70 \\ \end{align*}