Internal problem ID [539]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 10.
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: 0.016 (sec). Leaf size: 29
dsolve(diff(y(t),t) = y(t)*(1-y(t)^2),y(t), singsol=all)
\begin{align*} y \relax (t ) = \frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 t}+1}} \\ y \relax (t ) = -\frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 t}+1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.723 (sec). Leaf size: 100
DSolve[y'[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*}