72.5.1 problem 1 and 13 (i)

Internal problem ID [14608]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 1 and 13 (i)
Date solved : Thursday, March 13, 2025 at 04:08:46 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 y \left (y-2\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 14

ode:=diff(y(t),t) = 3*y(t)*(y(t)-2); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {2}{1+{\mathrm e}^{6 t}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 16

ode=D[y[t],t]==3*y[t]*(y[t]-2); 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {2}{e^{6 t}+1} \]

✓ Sympy. Time used: 0.329 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*(y(t) - 2)*y(t) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {2}{- e^{6 t} - 1} \]