27.1.3 problem 3

Internal problem ID [4297]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.1
Problem number : 3
Date solved : Monday, January 27, 2025 at 08:50:10 AM
CAS classification : [_linear]

\begin{align*} \ln \left (x \right ) y^{\prime }+\frac {x +y}{x}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(ln(x)*diff(y(x),x)+(x+y(x))/x=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 16

DSolve[Log[x]*D[y[x],x]+(x+y[x])/x==0,y[x],x,IncludeSingularSolutions -> True]
 

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