90.1.23 problem 34

Internal problem ID [25047]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 34
Date solved : Thursday, October 02, 2025 at 11:47:49 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 12

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

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

✓ Sympy. Time used: 0.175 (sec). Leaf size: 12

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

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