76.3.20 problem 20

Internal problem ID [17391]
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 : 20
Date solved : Tuesday, January 28, 2025 at 10:04:18 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 40

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