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 : Wednesday, March 05, 2025 at 04:05:48 AM
CAS classification : [_quadrature]

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

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

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

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

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

ode=D[q[t],t]==k*(q[t]-70); 
ic={}; 
DSolve[{ode,ic},q[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.151 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
k = symbols("k") 
q = Function("q") 
ode = Eq(-k*(q(t) - 70) + Derivative(q(t), t),0) 
ics = {} 
dsolve(ode,func=q(t),ics=ics)
 

\[ q{\left (t \right )} = C_{1} e^{k t} + 70 \]