35.3.8 problem 8

Internal problem ID [6112]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 8
Date solved : Monday, January 27, 2025 at 01:36:24 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {\ln \left (x \right )}{2}+\frac {c_1}{\ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 19

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

\[ y(x)\to \frac {\log (x)}{2}+\frac {c_1}{\log (x)} \]