68.4.40 problem 40

Internal problem ID [17220]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 40
Date solved : Thursday, October 02, 2025 at 01:58:45 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{3}+y \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(y(t),t) = y(t)^3+y(t); 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {{\mathrm e}^{-2 t} c_1 -1}} \\ y &= -\frac {1}{\sqrt {{\mathrm e}^{-2 t} c_1 -1}} \\ \end{align*}

✓ Mathematica. Time used: 0.089 (sec). Leaf size: 51

ode=D[y[t],t]==y[t]^3+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] \left (K[1]^2+1\right )}dK[1]\&\right ][t+c_1]\\ y(t)&\to 0\\ y(t)&\to -i\\ y(t)&\to i \end{align*}

✓ Sympy. Time used: 0.579 (sec). Leaf size: 36

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**3 - y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ \left [ y{\left (t \right )} = - \sqrt {\frac {e^{2 t}}{C_{1} - e^{2 t}}}, \ y{\left (t \right )} = \sqrt {\frac {e^{2 t}}{C_{1} - e^{2 t}}}\right ] \]