57.4.21 problem 10(b)

Internal problem ID [14345]
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 : Thursday, October 02, 2025 at 09:32:00 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,op(ic)],T(t), singsol=all);
 

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

✓ Mathematica. Time used: 1.078 (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]
 

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

✗ 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