57.3.5 problem 4(b)

Internal problem ID [14321]
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 1.2 Antiderivatives. Exercises page 19
Problem number : 4(b)
Date solved : Thursday, October 02, 2025 at 09:31:30 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=diff(x(t),t) = 1/t/ln(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \ln \left (\ln \left (t \right )\right )+c_1 \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 11

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

\begin{align*} x(t)&\to \log (\log (t))+c_1 \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 8

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

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