72.5.2 problem 1 and 13 (ii)

Internal problem ID [14609]
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 (ii)
Date solved : Thursday, March 13, 2025 at 04:08:50 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-2\right )&=-1 \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 18

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

\[ y = -\frac {2}{3 \,{\mathrm e}^{12+6 t}-1} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 20

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

\[ y(t)\to \frac {2}{1-3 e^{6 (t+2)}} \]

✓ Sympy. Time used: 0.353 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = \frac {2}{3 \left (- e^{6 t} + \frac {1}{3 e^{12}}\right ) e^{12}} \]