71.2.7 problem 7

Internal problem ID [14339]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:27:02 AM
CAS classification : [_separable]

\begin{align*} x \ln \left (x \right ) y^{\prime }-\left (1+\ln \left (x \right )\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 9

dsolve((x*ln(x))*diff(y(x),x)-(1+ln(x))*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 17

DSolve[(x*Log[x])*D[y[x],x]-(1+Log[x])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e c_1 x \log (x) \\ y(x)\to 0 \\ \end{align*}