10.3.13 problem 17

Internal problem ID [1178]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 17
Date solved : Tuesday, March 04, 2025 at 12:17:08 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.232 (sec). Leaf size: 44

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

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

✓ Sympy. Time used: 1.571 (sec). Leaf size: 70

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

\[ \left [ y{\left (t \right )} = \frac {3 \left (- e^{3 t^{2}} - \sqrt {e^{C_{1} + 3 t^{2}}}\right )}{e^{C_{1}} - e^{3 t^{2}}}, \ y{\left (t \right )} = \frac {3 \left (- e^{3 t^{2}} + \sqrt {e^{C_{1} + 3 t^{2}}}\right )}{e^{C_{1}} - e^{3 t^{2}}}\right ] \]