76.5.32 problem 33

Internal problem ID [17452]
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 : Tuesday, January 28, 2025 at 10:38:45 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\[ y = -\ln \left (\ln \left (x \right )\right )+c_{1} \]

✓ Solution by Mathematica

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

DSolve[x*D[y[x],x]==-1/Log[x],y[x],x,IncludeSingularSolutions -> True]
 

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