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 : Saturday, March 29, 2025 at 10:44:47 PM
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: 0.122 (sec). Leaf size: 35

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

✓ Sympy. Time used: 0.257 (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)
 

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