15.8.4 problem 4

Internal problem ID [3007]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:07:37 AM
CAS classification : [_linear]

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

Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(x*ln(x)*diff(y(x),x)+(y(x)-x)=0,y(x), singsol=all)
 
\[ y = \frac {x +c_{1}}{\ln \left (x \right )} \]

Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 14

DSolve[x*Log[x]*D[y[x],x]+(y[x]-x)==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \frac {x+c_1}{\log (x)} \]