Internal problem ID [4925]
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]
\[ \boxed {x^{\prime }-x^{3}-x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(x(t),t)-x(t)^3=x(t),x(t), singsol=all)
\begin{align*} x \left (t \right ) &= \frac {1}{\sqrt {{\mathrm e}^{-2 t} c_{1} -1}} \\ x \left (t \right ) &= -\frac {1}{\sqrt {{\mathrm e}^{-2 t} c_{1} -1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.064 (sec). Leaf size: 57
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)}}} \\ \end{align*}