76.3.21 problem 21

Internal problem ID [17392]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 10:04:20 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }&=-y \left (3-t y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(t),t)=-y(t)*(3-t*y(t)),y(t), singsol=all)
 

\[ y = \frac {9}{1+9 c_{1} {\mathrm e}^{3 t}+3 t} \]

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 39

DSolve[D[y[t],t]==-y[t]*(3-t*y[t]),y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {e^{-3 t}}{-\int _1^te^{-3 K[1]} K[1]dK[1]+c_1} \\ y(t)\to 0 \\ \end{align*}