7.6.3 problem 3

Internal problem ID [173]
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 : 3
Date solved : Friday, February 07, 2025 at 08:00:54 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=1-x^{2} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 9

dsolve([diff(x(t),t)=1-x(t)^2,x(0) = 3],x(t), singsol=all)
 

\[ x = \coth \left (t +\operatorname {arctanh}\left (\frac {1}{3}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 26

DSolve[{D[x[t],t]==1-x[t]^2,{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {2 e^{2 t}+1}{2 e^{2 t}-1} \]