76.3.20 problem 20

Internal problem ID [17312]
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 : Thursday, March 13, 2025 at 09:25:37 AM
CAS classification : [_Bernoulli]

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

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

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

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

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

ode=D[y[t],t]==y[t]*(3-t*y[t]); 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.254 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-(-t*y(t) + 3)*y(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {9 e^{3 t}}{C_{1} + 3 t e^{3 t} - e^{3 t}} \]