17.4.1 problem 1.1-5

Internal problem ID [3433]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-5, page 7
Problem number : 1.1-5
Date solved : Tuesday, March 04, 2025 at 04:38:40 PM
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: 0.21 (sec). Leaf size: 25

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

\begin{align*} y(t)\to \frac {1}{1+e^{t+c_1}} \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}

✓ Sympy. Time used: 0.274 (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)
 

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