Internal problem ID [4469]
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]
Solve \begin {gather*} \boxed {u^{\prime }-\alpha \left (1-u\right )+\beta u=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 21
dsolve(diff(u(t),t)=alpha*(1-u(t))-beta*u(t),u(t), singsol=all)
\[ u \relax (t ) = \frac {\alpha }{\alpha +\beta }+{\mathrm e}^{-\left (\alpha +\beta \right ) t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.047 (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*}