74.4.5 problem 5

Internal problem ID [19842]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85
Problem number : 5
Date solved : Thursday, October 02, 2025 at 04:48:11 PM
CAS classification : [_Bernoulli]

\begin{align*} \left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=(T(t)*ln(t)-1)*T(t) = t*diff(T(t),t); 
dsolve(ode,T(t), singsol=all);
 

\[ T = \frac {1}{1+c_1 t +\ln \left (t \right )} \]

✓ Mathematica. Time used: 0.095 (sec). Leaf size: 20

ode=(T[t]*Log[t]-1)*T[t]==t*D[T[t],t]; 
ic={}; 
DSolve[{ode,ic},T[t],t,IncludeSingularSolutions->True]
 

\begin{align*} T(t)&\to \frac {1}{\log (t)+c_1 t+1}\\ T(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 12

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

\[ T{\left (t \right )} = \frac {1}{C_{1} t + \log {\left (t \right )} + 1} \]