66.2.17 problem 16 (ii)

Internal problem ID [15939]
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 : 16 (ii)
Date solved : Thursday, October 02, 2025 at 10:31:18 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

ode:=diff(y(t),t) = y(t)^2-y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {1}{1+{\mathrm e}^{t} c_1} \]

✓ Mathematica. Time used: 0.111 (sec). Leaf size: 40

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

\begin{align*} y(t)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ][t+c_1]\\ y(t)&\to 0\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.170 (sec). Leaf size: 8

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

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