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 : Tuesday, March 04, 2025 at 10:56:42 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*}

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

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

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

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

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

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

✓ Sympy. Time used: 0.379 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq((3*x(t) - 15)*x(t) + Derivative(x(t), t),0) 
ics = {x(0): 2} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \frac {5}{1 + \frac {3 e^{- 15 t}}{2}} \]