56.4.63 problem 60

Internal problem ID [8952]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 60
Date solved : Monday, January 27, 2025 at 05:20:43 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \left (1-y^{2}\right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x)=y(x)*(1-y(x)^2),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: 0.731 (sec). Leaf size: 100

DSolve[D[y[x],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*}