Internal problem ID [6531]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 60.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y \left (1-y^{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(diff(y(x),x)=y(x)*(1-y(x)^2),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 x}+1}} \\ y \relax (x ) = -\frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 x}+1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.223 (sec). Leaf size: 100
DSolve[y'[x]==y[x]*(1-y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^x}{\sqrt {e^{2 x}+e^{2 c_1}}} \\ y(x)\to \frac {e^x}{\sqrt {e^{2 x}+e^{2 c_1}}} \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ y(x)\to -\frac {e^x}{\sqrt {e^{2 x}}} \\ y(x)\to \frac {e^x}{\sqrt {e^{2 x}}} \\ \end{align*}