10.4.2 problem 3

Internal problem ID [1183]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.5. Page 88
Problem number : 3
Date solved : Monday, January 27, 2025 at 04:39:38 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.149 (sec). Leaf size: 75

dsolve(diff(y(t),t) = y(t)*(-2+y(t))*(-1+y(t)),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 10.200 (sec). Leaf size: 100

DSolve[D[y[t],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*}