10.4.8 problem 10

Internal problem ID [1189]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:43:28 AM
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(t),t) = y(t)*(1-y(t)^2),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.666 (sec). Leaf size: 100

DSolve[D[y[t],t]== y[t]*(1-y[t]^2),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\frac {e^t}{\sqrt {e^{2 t}+e^{2 c_1}}} \\ y(t)\to \frac {e^t}{\sqrt {e^{2 t}+e^{2 c_1}}} \\ y(t)\to -1 \\ y(t)\to 0 \\ y(t)\to 1 \\ y(t)\to -\frac {e^t}{\sqrt {e^{2 t}}} \\ y(t)\to \frac {e^t}{\sqrt {e^{2 t}}} \\ \end{align*}