Internal problem ID [14197]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{3}+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(t),t)=y(t)^3-y(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {1}{\sqrt {c_{1} {\mathrm e}^{2 t}+1}} \\ y \left (t \right ) &= -\frac {1}{\sqrt {c_{1} {\mathrm e}^{2 t}+1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.714 (sec). Leaf size: 54
DSolve[y'[t]==y[t]^3-y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {1}{\sqrt {1+e^{2 (t+c_1)}}} \\ y(t)\to \frac {1}{\sqrt {1+e^{2 (t+c_1)}}} \\ y(t)\to -1 \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}