1.6.4 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 : Tuesday, September 30, 2025 at 03:48:19 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*}

✓ Maple. Time used: 0.087 (sec). Leaf size: 10

ode:=diff(x(t),t) = 9-4*x(t)^2; 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = \frac {3 \tanh \left (6 t \right )}{2} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 23

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

\begin{align*} x(t)&\to \frac {3 \left (e^{6 t}-1\right )}{e^{6 t}+1} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(4*x(t)**2 + Derivative(x(t), t) - 9,0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants