57.4.8 problem 1(h)

Internal problem ID [14332]
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 1.3.1 Separable equations. Exercises page 26
Problem number : 1(h)
Date solved : Thursday, October 02, 2025 at 09:31:40 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=r \left (a -y\right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(t),t) = r*(a-y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = a +{\mathrm e}^{-r t} c_1 \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 21

ode=D[y[t],t]==r*(a-y[t]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to a+c_1 e^{-r t}\\ y(t)&\to a \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
a = symbols("a") 
r = symbols("r") 
y = Function("y") 
ode = Eq(-r*(a - y(t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- r t} + a \]