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]
\[ \boxed {y^{\prime }-y \left (-2+y\right ) \left (y-1\right )=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 73
dsolve(diff(y(t),t) = y(t)*(-2+y(t))*(-1+y(t)),y(t), singsol=all)
\begin{align*} y \left (t \right ) = -\frac {{\mathrm e}^{2 t} c_{1}}{\left (-\frac {1}{\sqrt {-c_{1} {\mathrm e}^{2 t}+1}}-1\right ) \left (c_{1} {\mathrm e}^{2 t}-1\right )} y \left (t \right ) = -\frac {{\mathrm e}^{2 t} c_{1}}{\left (\frac {1}{\sqrt {-c_{1} {\mathrm e}^{2 t}+1}}-1\right ) \left (c_{1} {\mathrm e}^{2 t}-1\right )} \end{align*}
✓ Solution by Mathematica
Time used: 11.055 (sec). Leaf size: 100
DSolve[y'[t] == y[t]*(-2+y[t])*(-1+y[t]),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {-\sqrt {1+e^{2 (t+c_1)}}+e^{2 (t+c_1)}+1}{1+e^{2 (t+c_1)}} y(t)\to \frac {\sqrt {1+e^{2 (t+c_1)}}+e^{2 (t+c_1)}+1}{1+e^{2 (t+c_1)}} y(t)\to 0 y(t)\to 1 y(t)\to 2 \end{align*}