Internal problem ID [11375]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-r \left (a -y\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(t),t)=r*(a-y(t)),y(t), singsol=all)
\[ y \left (t \right ) = a +{\mathrm e}^{-r t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 21
DSolve[y'[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*}