8.5.21 problem 21

Internal problem ID [749]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 21
Date solved : Wednesday, February 05, 2025 at 03:57:34 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 60.063 (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*}