80.4.5 problem 5

Internal problem ID [18556]
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 : Tuesday, January 28, 2025 at 11:58:47 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.136 (sec). Leaf size: 20

DSolve[(T[t]*Log[t]-1)*T[t]==t*D[T[t],t],T[t],t,IncludeSingularSolutions -> True]
 

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