63.4.8 problem 1(h)

Internal problem ID [13051]
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 : Tuesday, January 28, 2025 at 04:50:14 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\[ y = a +{\mathrm e}^{-r t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 21

DSolve[D[y[t],t]==r*(a-y[t]),y[t],t,IncludeSingularSolutions -> True]
 

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