90.2.3 problem 3

Internal problem ID [25054]
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 23
Problem number : 3
Date solved : Thursday, October 02, 2025 at 11:47:55 PM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }&=y \left (t +y\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

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

\[ y = \frac {2 \,{\mathrm e}^{\frac {t^{2}}{2}}}{i \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right )+2 c_1} \]

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 0.178 (sec). Leaf size: 10

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

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