10.2.28 problem 28

Internal problem ID [1156]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 28
Date solved : Saturday, March 29, 2025 at 10:42:47 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\[ y = \frac {4}{1+4 \,{\mathrm e}^{-4 t} \left (1+t \right )^{4} c_1} \]

✓ Mathematica. Time used: 3.294 (sec). Leaf size: 42

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

\begin{align*} y(t)\to \frac {4 e^{4 t}}{e^{4 t}+e^{4 c_1} (t+1)^4} \\ y(t)\to 0 \\ y(t)\to 4 \\ \end{align*}

✓ Sympy. Time used: 0.526 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*(4 - y(t))*y(t)/(t + 1) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {4}{C_{1} \left (t + 1\right )^{4} e^{- 4 t} - 1} \]