90.3.2 problem 2

Internal problem ID [25066]
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 41
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:48:11 PM
CAS classification : [_quadrature]

\begin{align*} y y^{\prime }&=1-y \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 17

ode:=y(t)*diff(y(t),t) = 1-y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \operatorname {LambertW}\left (\frac {{\mathrm e}^{-t -1}}{c_1}\right )+1 \]

✓ Mathematica. Time used: 1.324 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to 1+W\left (e^{-t-1+c_1}\right )\\ y(t)&\to 1 \end{align*}

✓ Sympy. Time used: 0.220 (sec). Leaf size: 14

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

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