36.1.14 problem 14

Internal problem ID [6269]
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
Date solved : Monday, January 27, 2025 at 01:52:27 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.007 (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: 60.065 (sec). Leaf size: 57

DSolve[D[x[t],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*}