68.1.30 problem 37

Internal problem ID [17097]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 37
Date solved : Thursday, October 02, 2025 at 01:43:11 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 11

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

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

✓ Sympy. Time used: 0.082 (sec). Leaf size: 8

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

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