10.2.27 problem 27

Internal problem ID [1155]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 27
Date solved : Saturday, March 29, 2025 at 10:42:44 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 19

ode:=diff(y(t),t) = 1/3*t*(4-y(t))*y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {4}{1+4 \,{\mathrm e}^{-\frac {2 t^{2}}{3}} c_1} \]

✓ Mathematica. Time used: 0.249 (sec). Leaf size: 44

ode=D[y[t],t]== 1/3*t*(4-y[t])*y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)\to \frac {4 e^{\frac {2 t^2}{3}}}{e^{\frac {2 t^2}{3}}+e^{4 c_1}} \\ y(t)\to 0 \\ y(t)\to 4 \\ \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*(4 - y(t))*y(t)/3 + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out