Internal problem ID [4417]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x^{\prime }-x^{3}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 29
dsolve(diff(x(t),t)-x(t)^3=x(t),x(t), singsol=all)
\begin{align*} x \relax (t ) = \frac {1}{\sqrt {{\mathrm e}^{-2 t} c_{1}-1}} \\ x \relax (t ) = -\frac {1}{\sqrt {{\mathrm e}^{-2 t} c_{1}-1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.184 (sec). Leaf size: 76
DSolve[x'[t]-x[t]^3==x[t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {i e^{t+c_1}}{\sqrt {-1+e^{2 (t+c_1)}}} \\ x(t)\to \frac {i e^{t+c_1}}{\sqrt {-1+e^{2 (t+c_1)}}} \\ x(t)\to 0 \\ x(t)\to -i \\ x(t)\to i \\ \end{align*}