Internal problem ID [533]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.5. Page 88
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y \left (-2+y\right ) \left (y-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 73
dsolve(diff(y(t),t) = y(t)*(-2+y(t))*(-1+y(t)),y(t), singsol=all)
\begin{align*} y \relax (t ) = -\frac {{\mathrm e}^{2 t} c_{1}}{\left (c_{1} {\mathrm e}^{2 t}-1\right ) \left (-\frac {1}{\sqrt {1-c_{1} {\mathrm e}^{2 t}}}-1\right )} \\ y \relax (t ) = -\frac {{\mathrm e}^{2 t} c_{1}}{\left (c_{1} {\mathrm e}^{2 t}-1\right ) \left (\frac {1}{\sqrt {1-c_{1} {\mathrm e}^{2 t}}}-1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 12.063 (sec). Leaf size: 58
DSolve[y'[t] == y[t]*(-2+y[t])*(-1+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 1-\frac {1}{\sqrt {1+e^{2 (t+c_1)}}} \\ y(t)\to 1+\frac {1}{\sqrt {1+e^{2 (t+c_1)}}} \\ y(t)\to 0 \\ y(t)\to 1 \\ y(t)\to 2 \\ \end{align*}