Internal problem ID [99]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y-y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 29
dsolve(diff(y(x),x) = y(x)+y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {{\mathrm e}^{-2 x} c_{1}-1}} \\ y \relax (x ) = -\frac {1}{\sqrt {{\mathrm e}^{-2 x} c_{1}-1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.653 (sec). Leaf size: 76
DSolve[y'[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)}}} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}