7.6.6 problem 6

Internal problem ID [176]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.7 (population models). Problems at page 82
Problem number : 6
Date solved : Friday, February 07, 2025 at 08:01:08 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=3 x \left (5-x\right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 16

dsolve([diff(x(t),t)=3*x(t)*(5-x(t)),x(0) = 2],x(t), singsol=all)
 

\[ x = \frac {10}{2+3 \,{\mathrm e}^{-15 t}} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 23

DSolve[{D[x[t],t]==3*x[t]*(5-x[t]),{x[0]==2}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {10 e^{15 t}}{2 e^{15 t}+3} \]