36.2.28 problem 40

Internal problem ID [6321]
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
Date solved : Monday, January 27, 2025 at 01:56:29 PM
CAS classification : [_quadrature]

\begin{align*} u^{\prime }&=\alpha \left (1-u\right )-\beta u \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(u(t),t)=alpha*(1-u(t))-beta*u(t),u(t), singsol=all)
 

\[ u = \frac {c_{1} \left (\alpha +\beta \right ) {\mathrm e}^{-\left (\alpha +\beta \right ) t}+\alpha }{\alpha +\beta } \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 35

DSolve[D[u[t],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*}