66.2.7 problem 7

Internal problem ID [15929]
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 1.3 page 47
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:30:13 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 y \left (1-y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \\ \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 12

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

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

✗ Mathematica

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

{}

✓ Sympy. Time used: 0.267 (sec). Leaf size: 12

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

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