10.3.14 problem 18

Internal problem ID [1179]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 18
Date solved : Monday, January 27, 2025 at 04:39:31 AM
CAS classification : [_Bernoulli]

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

\[ y = \frac {9}{-1+9 c_1 \,{\mathrm e}^{-3 t}+3 t} \]

✓ Solution by Mathematica

Time used: 0.122 (sec). Leaf size: 35

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

\begin{align*} y(t)\to \frac {9 e^{3 t}}{e^{3 t} (3 t-1)+9 c_1} \\ y(t)\to 0 \\ \end{align*}