76.5.32 problem 33

Internal problem ID [17381]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 33
Date solved : Monday, March 31, 2025 at 04:10:38 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 13

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

\[ y(x)\to -\log (\log (x))+c_1 \]

✓ Sympy. Time used: 0.148 (sec). Leaf size: 8

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

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