Internal problem ID [4977]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises.
page 54
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {u^{\prime }-\alpha \left (1-u\right )+\beta u=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(u(t),t)=alpha*(1-u(t))-beta*u(t),u(t), singsol=all)
\[ u \left (t \right ) = \frac {c_{1} \left (\alpha +\beta \right ) {\mathrm e}^{-\left (\alpha +\beta \right ) t}+\alpha }{\alpha +\beta } \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 35
DSolve[u'[t]==\[Alpha]*(1-u[t])-\[Beta]*u[t],u[t],t,IncludeSingularSolutions -> True]
\begin{align*} u(t)\to \frac {\alpha }{\alpha +\beta }+c_1 e^{-t (\alpha +\beta )} \\ u(t)\to \frac {\alpha }{\alpha +\beta } \\ \end{align*}