Internal problem ID [14198]
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.
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 {{\mathrm e}^{-2 t} c_{1} -1}} \\ y \left (t \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{-2 t} c_{1} -1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.063 (sec). Leaf size: 57
DSolve[y'[t]==y[t]^3+y[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {i e^{t+c_1}}{\sqrt {-1+e^{2 (t+c_1)}}} \\ y(t)\to \frac {i e^{t+c_1}}{\sqrt {-1+e^{2 (t+c_1)}}} \\ \end{align*}