Internal problem ID [12283]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 1. Introduction. Exercises 1.3, page 27
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime } \ln \left (x \right )-\left (\ln \left (x \right )+1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve((x*ln(x))*diff(y(x),x)-(1+ln(x))*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.087 (sec). Leaf size: 16
DSolve[(x*Log[x])*y'[x]-(1+Log[x])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \log (x) y(x)\to 0 \end{align*}