74.4.39 problem 39

Internal problem ID [15932]
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 : 39
Date solved : Tuesday, January 28, 2025 at 08:23:19 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

dsolve(diff(y(t),t)=y(t)^3-y(t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.214 (sec). Leaf size: 51

DSolve[D[y[t],t]==y[t]^3-y[t],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1] (K[1]+1)}dK[1]\&\right ][t+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}