17.4.1 problem 1.1-5

Internal problem ID [3433]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-5, page 7
Problem number : 1.1-5
Date solved : Monday, January 27, 2025 at 07:36:33 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(diff(y(t),t)=y(t)^2-y(t),y(t), singsol=all)
 

\[ y = \frac {1}{1+{\mathrm e}^{t} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.210 (sec). Leaf size: 25

DSolve[D[y[t],t]==y[t]^2-y[t],y[t],t,IncludeSingularSolutions -> True]
 

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