63.4.21 problem 10(b)

Internal problem ID [12993]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 10(b)
Date solved : Monday, March 31, 2025 at 07:29:47 AM
CAS classification : [_separable]

\begin{align*} T^{\prime }&=2 a t \left (T^{2}-a^{2}\right ) \end{align*}

With initial conditions

\begin{align*} T \left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.238 (sec). Leaf size: 15

ode:=diff(T(t),t) = 2*a*t*(T(t)^2-a^2); 
ic:=T(0) = 0; 
dsolve([ode,ic],T(t), singsol=all);
 

\[ T = -a \tanh \left (t^{2} a^{2}\right ) \]

✓ Mathematica. Time used: 1.906 (sec). Leaf size: 16

ode=D[ T[t],t]==2*a*t*(T[t]^2-a^2); 
ic={T[0]==0}; 
DSolve[{ode,ic},T[t],t,IncludeSingularSolutions->True]
 

\[ T(t)\to -a \tanh \left (a^2 t^2\right ) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
T = Function("T") 
ode = Eq(-2*a*t*(-a**2 + T(t)**2) + Derivative(T(t), t),0) 
ics = {T(0): 0} 
dsolve(ode,func=T(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants