7.5.21 problem 21

Internal problem ID [125]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 21
Date solved : Friday, February 07, 2025 at 07:53:13 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y+y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(y(x),x)=y(x)+y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\sqrt {c_1 \,{\mathrm e}^{-2 x}-1}} \\ y &= -\frac {1}{\sqrt {c_1 \,{\mathrm e}^{-2 x}-1}} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==y[x]+y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {i e^{x+c_1}}{\sqrt {-1+e^{2 (x+c_1)}}} \\ y(x)\to \frac {i e^{x+c_1}}{\sqrt {-1+e^{2 (x+c_1)}}} \\ \end{align*}