7.6.4 problem 4

Internal problem ID [174]
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 : 4
Date solved : Friday, February 07, 2025 at 08:00:57 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=9-4 x^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.068 (sec). Leaf size: 23

dsolve([diff(x(t),t)=9-4*x(t)^2,x(0) = 0],x(t), singsol=all)
 

\[ x = \frac {-3+3 \,{\mathrm e}^{12 t}}{2 \,{\mathrm e}^{12 t}+2} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 23

DSolve[{D[x[t],t]==9-x[t]^2,{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {3 \left (e^{6 t}-1\right )}{e^{6 t}+1} \]